diff --git a/changelog.d/10598.feature b/changelog.d/10598.feature
new file mode 100644
index 000000000..92c159118
--- /dev/null
+++ b/changelog.d/10598.feature
@@ -0,0 +1 @@
+Allow editing a user's `external_ids` via the "Edit User" admin API. Contributed by @dklimpel.
\ No newline at end of file
diff --git a/docs/admin_api/user_admin_api.md b/docs/admin_api/user_admin_api.md
index 4b5dd4685..6a9335d6e 100644
--- a/docs/admin_api/user_admin_api.md
+++ b/docs/admin_api/user_admin_api.md
@@ -81,6 +81,16 @@ with a body of:
             "address": "<user_mail_2>"
         }
     ],
+    "external_ids": [
+        {
+            "auth_provider": "<provider1>",
+            "external_id": "<user_id_provider_1>"
+        },
+        {
+            "auth_provider": "<provider2>",
+            "external_id": "<user_id_provider_2>"
+        }
+    ],
     "avatar_url": "<avatar_url>",
     "admin": false,
     "deactivated": false
@@ -90,26 +100,34 @@ with a body of:
 To use it, you will need to authenticate by providing an `access_token` for a
 server admin: [Admin API](../usage/administration/admin_api)
 
+Returns HTTP status code:
+- `201` - When a new user object was created.
+- `200` - When a user was modified.
+
 URL parameters:
 
 - `user_id`: fully-qualified user id: for example, `@user:server.com`.
 
 Body parameters:
 
-- `password`, optional. If provided, the user's password is updated and all
+- `password` - string, optional. If provided, the user's password is updated and all
   devices are logged out.
-
-- `displayname`, optional, defaults to the value of `user_id`.
-
-- `threepids`, optional, allows setting the third-party IDs (email, msisdn)
+- `displayname` - string, optional, defaults to the value of `user_id`.
+- `threepids` - array, optional, allows setting the third-party IDs (email, msisdn)
+  - `medium` - string. Kind of third-party ID, either `email` or `msisdn`.
+  - `address` - string. Value of third-party ID.
   belonging to a user.
-
-- `avatar_url`, optional, must be a
+- `external_ids` - array, optional. Allow setting the identifier of the external identity
+  provider for SSO (Single sign-on). Details in
+  [Sample Configuration File](../usage/configuration/homeserver_sample_config.html)
+  section `sso` and `oidc_providers`.
+  - `auth_provider` - string. ID of the external identity provider. Value of `idp_id`
+    in homeserver configuration.
+  - `external_id` - string, user ID in the external identity provider.
+- `avatar_url` - string, optional, must be a
   [MXC URI](https://matrix.org/docs/spec/client_server/r0.6.0#matrix-content-mxc-uris).
-
-- `admin`, optional, defaults to `false`.
-
-- `deactivated`, optional. If unspecified, deactivation state will be left
+- `admin` - bool, optional, defaults to `false`.
+- `deactivated` - bool, optional. If unspecified, deactivation state will be left
   unchanged on existing accounts and set to `false` for new accounts.
   A user cannot be erased by deactivating with this API. For details on
   deactivating users see [Deactivate Account](#deactivate-account).
diff --git a/synapse/rest/admin/users.py b/synapse/rest/admin/users.py
index 41f21ba11..c885fd77a 100644
--- a/synapse/rest/admin/users.py
+++ b/synapse/rest/admin/users.py
@@ -196,20 +196,57 @@ class UserRestServletV2(RestServlet):
         user = await self.admin_handler.get_user(target_user)
         user_id = target_user.to_string()
 
+        # check for required parameters for each threepid
+        threepids = body.get("threepids")
+        if threepids is not None:
+            for threepid in threepids:
+                assert_params_in_dict(threepid, ["medium", "address"])
+
+        # check for required parameters for each external_id
+        external_ids = body.get("external_ids")
+        if external_ids is not None:
+            for external_id in external_ids:
+                assert_params_in_dict(external_id, ["auth_provider", "external_id"])
+
+        user_type = body.get("user_type", None)
+        if user_type is not None and user_type not in UserTypes.ALL_USER_TYPES:
+            raise SynapseError(400, "Invalid user type")
+
+        set_admin_to = body.get("admin", False)
+        if not isinstance(set_admin_to, bool):
+            raise SynapseError(
+                HTTPStatus.BAD_REQUEST,
+                "Param 'admin' must be a boolean, if given",
+                Codes.BAD_JSON,
+            )
+
+        password = body.get("password", None)
+        if password is not None:
+            if not isinstance(password, str) or len(password) > 512:
+                raise SynapseError(400, "Invalid password")
+
+        deactivate = body.get("deactivated", False)
+        if not isinstance(deactivate, bool):
+            raise SynapseError(400, "'deactivated' parameter is not of type boolean")
+
+        # convert into List[Tuple[str, str]]
+        if external_ids is not None:
+            new_external_ids = []
+            for external_id in external_ids:
+                new_external_ids.append(
+                    (external_id["auth_provider"], external_id["external_id"])
+                )
+
         if user:  # modify user
             if "displayname" in body:
                 await self.profile_handler.set_displayname(
                     target_user, requester, body["displayname"], True
                 )
 
-            if "threepids" in body:
-                # check for required parameters for each threepid
-                for threepid in body["threepids"]:
-                    assert_params_in_dict(threepid, ["medium", "address"])
-
+            if threepids is not None:
                 # remove old threepids from user
-                threepids = await self.store.user_get_threepids(user_id)
-                for threepid in threepids:
+                old_threepids = await self.store.user_get_threepids(user_id)
+                for threepid in old_threepids:
                     try:
                         await self.auth_handler.delete_threepid(
                             user_id, threepid["medium"], threepid["address"], None
@@ -220,18 +257,39 @@ class UserRestServletV2(RestServlet):
 
                 # add new threepids to user
                 current_time = self.hs.get_clock().time_msec()
-                for threepid in body["threepids"]:
+                for threepid in threepids:
                     await self.auth_handler.add_threepid(
                         user_id, threepid["medium"], threepid["address"], current_time
                     )
 
-            if "avatar_url" in body and type(body["avatar_url"]) == str:
+            if external_ids is not None:
+                # get changed external_ids (added and removed)
+                cur_external_ids = await self.store.get_external_ids_by_user(user_id)
+                add_external_ids = set(new_external_ids) - set(cur_external_ids)
+                del_external_ids = set(cur_external_ids) - set(new_external_ids)
+
+                # remove old external_ids
+                for auth_provider, external_id in del_external_ids:
+                    await self.store.remove_user_external_id(
+                        auth_provider,
+                        external_id,
+                        user_id,
+                    )
+
+                # add new external_ids
+                for auth_provider, external_id in add_external_ids:
+                    await self.store.record_user_external_id(
+                        auth_provider,
+                        external_id,
+                        user_id,
+                    )
+
+            if "avatar_url" in body and isinstance(body["avatar_url"], str):
                 await self.profile_handler.set_avatar_url(
                     target_user, requester, body["avatar_url"], True
                 )
 
             if "admin" in body:
-                set_admin_to = bool(body["admin"])
                 if set_admin_to != user["admin"]:
                     auth_user = requester.user
                     if target_user == auth_user and not set_admin_to:
@@ -239,29 +297,18 @@ class UserRestServletV2(RestServlet):
 
                     await self.store.set_server_admin(target_user, set_admin_to)
 
-            if "password" in body:
-                if not isinstance(body["password"], str) or len(body["password"]) > 512:
-                    raise SynapseError(400, "Invalid password")
-                else:
-                    new_password = body["password"]
-                    logout_devices = True
+            if password is not None:
+                logout_devices = True
+                new_password_hash = await self.auth_handler.hash(password)
 
-                    new_password_hash = await self.auth_handler.hash(new_password)
-
-                    await self.set_password_handler.set_password(
-                        target_user.to_string(),
-                        new_password_hash,
-                        logout_devices,
-                        requester,
-                    )
+                await self.set_password_handler.set_password(
+                    target_user.to_string(),
+                    new_password_hash,
+                    logout_devices,
+                    requester,
+                )
 
             if "deactivated" in body:
-                deactivate = body["deactivated"]
-                if not isinstance(deactivate, bool):
-                    raise SynapseError(
-                        400, "'deactivated' parameter is not of type boolean"
-                    )
-
                 if deactivate and not user["deactivated"]:
                     await self.deactivate_account_handler.deactivate_account(
                         target_user.to_string(), False, requester, by_admin=True
@@ -285,36 +332,24 @@ class UserRestServletV2(RestServlet):
             return 200, user
 
         else:  # create user
-            password = body.get("password")
-            password_hash = None
-            if password is not None:
-                if not isinstance(password, str) or len(password) > 512:
-                    raise SynapseError(400, "Invalid password")
-                password_hash = await self.auth_handler.hash(password)
-
-            admin = body.get("admin", None)
-            user_type = body.get("user_type", None)
             displayname = body.get("displayname", None)
 
-            if user_type is not None and user_type not in UserTypes.ALL_USER_TYPES:
-                raise SynapseError(400, "Invalid user type")
+            password_hash = None
+            if password is not None:
+                password_hash = await self.auth_handler.hash(password)
 
             user_id = await self.registration_handler.register_user(
                 localpart=target_user.localpart,
                 password_hash=password_hash,
-                admin=bool(admin),
+                admin=set_admin_to,
                 default_display_name=displayname,
                 user_type=user_type,
                 by_admin=True,
             )
 
-            if "threepids" in body:
-                # check for required parameters for each threepid
-                for threepid in body["threepids"]:
-                    assert_params_in_dict(threepid, ["medium", "address"])
-
+            if threepids is not None:
                 current_time = self.hs.get_clock().time_msec()
-                for threepid in body["threepids"]:
+                for threepid in threepids:
                     await self.auth_handler.add_threepid(
                         user_id, threepid["medium"], threepid["address"], current_time
                     )
@@ -334,6 +369,14 @@ class UserRestServletV2(RestServlet):
                             data={},
                         )
 
+            if external_ids is not None:
+                for auth_provider, external_id in new_external_ids:
+                    await self.store.record_user_external_id(
+                        auth_provider,
+                        external_id,
+                        user_id,
+                    )
+
             if "avatar_url" in body and isinstance(body["avatar_url"], str):
                 await self.profile_handler.set_avatar_url(
                     target_user, requester, body["avatar_url"], True
diff --git a/synapse/storage/databases/main/registration.py b/synapse/storage/databases/main/registration.py
index 14670c288..c67bea81c 100644
--- a/synapse/storage/databases/main/registration.py
+++ b/synapse/storage/databases/main/registration.py
@@ -599,6 +599,28 @@ class RegistrationWorkerStore(CacheInvalidationWorkerStore):
             desc="record_user_external_id",
         )
 
+    async def remove_user_external_id(
+        self, auth_provider: str, external_id: str, user_id: str
+    ) -> None:
+        """Remove a mapping from an external user id to a mxid
+
+        If the mapping is not found, this method does nothing.
+
+        Args:
+            auth_provider: identifier for the remote auth provider
+            external_id: id on that system
+            user_id: complete mxid that it is mapped to
+        """
+        await self.db_pool.simple_delete(
+            table="user_external_ids",
+            keyvalues={
+                "auth_provider": auth_provider,
+                "external_id": external_id,
+                "user_id": user_id,
+            },
+            desc="remove_user_external_id",
+        )
+
     async def get_user_by_external_id(
         self, auth_provider: str, external_id: str
     ) -> Optional[str]:
diff --git a/tests/rest/admin/test_user.py b/tests/rest/admin/test_user.py
index 13fab5579..a736ec475 100644
--- a/tests/rest/admin/test_user.py
+++ b/tests/rest/admin/test_user.py
@@ -1240,6 +1240,101 @@ class UserRestTestCase(unittest.HomeserverTestCase):
         self.assertEqual(404, channel.code, msg=channel.json_body)
         self.assertEqual("M_NOT_FOUND", channel.json_body["errcode"])
 
+    def test_invalid_parameter(self):
+        """
+        If parameters are invalid, an error is returned.
+        """
+
+        # admin not bool
+        channel = self.make_request(
+            "PUT",
+            self.url_other_user,
+            access_token=self.admin_user_tok,
+            content={"admin": "not_bool"},
+        )
+        self.assertEqual(400, channel.code, msg=channel.json_body)
+        self.assertEqual(Codes.BAD_JSON, channel.json_body["errcode"])
+
+        # deactivated not bool
+        channel = self.make_request(
+            "PUT",
+            self.url_other_user,
+            access_token=self.admin_user_tok,
+            content={"deactivated": "not_bool"},
+        )
+        self.assertEqual(400, channel.code, msg=channel.json_body)
+        self.assertEqual(Codes.UNKNOWN, channel.json_body["errcode"])
+
+        # password not str
+        channel = self.make_request(
+            "PUT",
+            self.url_other_user,
+            access_token=self.admin_user_tok,
+            content={"password": True},
+        )
+        self.assertEqual(400, channel.code, msg=channel.json_body)
+        self.assertEqual(Codes.UNKNOWN, channel.json_body["errcode"])
+
+        # password not length
+        channel = self.make_request(
+            "PUT",
+            self.url_other_user,
+            access_token=self.admin_user_tok,
+            content={"password": "x" * 513},
+        )
+        self.assertEqual(400, channel.code, msg=channel.json_body)
+        self.assertEqual(Codes.UNKNOWN, channel.json_body["errcode"])
+
+        # user_type not valid
+        channel = self.make_request(
+            "PUT",
+            self.url_other_user,
+            access_token=self.admin_user_tok,
+            content={"user_type": "new type"},
+        )
+        self.assertEqual(400, channel.code, msg=channel.json_body)
+        self.assertEqual(Codes.UNKNOWN, channel.json_body["errcode"])
+
+        # external_ids not valid
+        channel = self.make_request(
+            "PUT",
+            self.url_other_user,
+            access_token=self.admin_user_tok,
+            content={
+                "external_ids": {"auth_provider": "prov", "wrong_external_id": "id"}
+            },
+        )
+        self.assertEqual(400, channel.code, msg=channel.json_body)
+        self.assertEqual(Codes.MISSING_PARAM, channel.json_body["errcode"])
+
+        channel = self.make_request(
+            "PUT",
+            self.url_other_user,
+            access_token=self.admin_user_tok,
+            content={"external_ids": {"external_id": "id"}},
+        )
+        self.assertEqual(400, channel.code, msg=channel.json_body)
+        self.assertEqual(Codes.MISSING_PARAM, channel.json_body["errcode"])
+
+        # threepids not valid
+        channel = self.make_request(
+            "PUT",
+            self.url_other_user,
+            access_token=self.admin_user_tok,
+            content={"threepids": {"medium": "email", "wrong_address": "id"}},
+        )
+        self.assertEqual(400, channel.code, msg=channel.json_body)
+        self.assertEqual(Codes.MISSING_PARAM, channel.json_body["errcode"])
+
+        channel = self.make_request(
+            "PUT",
+            self.url_other_user,
+            access_token=self.admin_user_tok,
+            content={"threepids": {"address": "value"}},
+        )
+        self.assertEqual(400, channel.code, msg=channel.json_body)
+        self.assertEqual(Codes.MISSING_PARAM, channel.json_body["errcode"])
+
     def test_get_user(self):
         """
         Test a simple get of a user.
@@ -1255,43 +1350,6 @@ class UserRestTestCase(unittest.HomeserverTestCase):
         self.assertEqual("User", channel.json_body["displayname"])
         self._check_fields(channel.json_body)
 
-    def test_get_user_with_sso(self):
-        """
-        Test get a user with SSO details.
-        """
-        self.get_success(
-            self.store.record_user_external_id(
-                "auth_provider1", "external_id1", self.other_user
-            )
-        )
-        self.get_success(
-            self.store.record_user_external_id(
-                "auth_provider2", "external_id2", self.other_user
-            )
-        )
-
-        channel = self.make_request(
-            "GET",
-            self.url_other_user,
-            access_token=self.admin_user_tok,
-        )
-
-        self.assertEqual(200, channel.code, msg=channel.json_body)
-        self.assertEqual("@user:test", channel.json_body["name"])
-        self.assertEqual(
-            "external_id1", channel.json_body["external_ids"][0]["external_id"]
-        )
-        self.assertEqual(
-            "auth_provider1", channel.json_body["external_ids"][0]["auth_provider"]
-        )
-        self.assertEqual(
-            "external_id2", channel.json_body["external_ids"][1]["external_id"]
-        )
-        self.assertEqual(
-            "auth_provider2", channel.json_body["external_ids"][1]["auth_provider"]
-        )
-        self._check_fields(channel.json_body)
-
     def test_create_server_admin(self):
         """
         Check that a new admin user is created successfully.
@@ -1353,6 +1411,12 @@ class UserRestTestCase(unittest.HomeserverTestCase):
             "admin": False,
             "displayname": "Bob's name",
             "threepids": [{"medium": "email", "address": "bob@bob.bob"}],
+            "external_ids": [
+                {
+                    "external_id": "external_id1",
+                    "auth_provider": "auth_provider1",
+                },
+            ],
             "avatar_url": "mxc://fibble/wibble",
         }
 
@@ -1368,6 +1432,12 @@ class UserRestTestCase(unittest.HomeserverTestCase):
         self.assertEqual("Bob's name", channel.json_body["displayname"])
         self.assertEqual("email", channel.json_body["threepids"][0]["medium"])
         self.assertEqual("bob@bob.bob", channel.json_body["threepids"][0]["address"])
+        self.assertEqual(
+            "external_id1", channel.json_body["external_ids"][0]["external_id"]
+        )
+        self.assertEqual(
+            "auth_provider1", channel.json_body["external_ids"][0]["auth_provider"]
+        )
         self.assertFalse(channel.json_body["admin"])
         self.assertEqual("mxc://fibble/wibble", channel.json_body["avatar_url"])
         self._check_fields(channel.json_body)
@@ -1632,6 +1702,103 @@ class UserRestTestCase(unittest.HomeserverTestCase):
         self.assertEqual("email", channel.json_body["threepids"][0]["medium"])
         self.assertEqual("bob3@bob.bob", channel.json_body["threepids"][0]["address"])
 
+    def test_set_external_id(self):
+        """
+        Test setting external id for an other user.
+        """
+
+        # Add two external_ids
+        channel = self.make_request(
+            "PUT",
+            self.url_other_user,
+            access_token=self.admin_user_tok,
+            content={
+                "external_ids": [
+                    {
+                        "external_id": "external_id1",
+                        "auth_provider": "auth_provider1",
+                    },
+                    {
+                        "external_id": "external_id2",
+                        "auth_provider": "auth_provider2",
+                    },
+                ]
+            },
+        )
+
+        self.assertEqual(200, channel.code, msg=channel.json_body)
+        self.assertEqual("@user:test", channel.json_body["name"])
+        self.assertEqual(2, len(channel.json_body["external_ids"]))
+        # result does not always have the same sort order, therefore it becomes sorted
+        self.assertEqual(
+            sorted(channel.json_body["external_ids"], key=lambda k: k["auth_provider"]),
+            [
+                {"auth_provider": "auth_provider1", "external_id": "external_id1"},
+                {"auth_provider": "auth_provider2", "external_id": "external_id2"},
+            ],
+        )
+        self._check_fields(channel.json_body)
+
+        # Set a new and remove an external_id
+        channel = self.make_request(
+            "PUT",
+            self.url_other_user,
+            access_token=self.admin_user_tok,
+            content={
+                "external_ids": [
+                    {
+                        "external_id": "external_id2",
+                        "auth_provider": "auth_provider2",
+                    },
+                    {
+                        "external_id": "external_id3",
+                        "auth_provider": "auth_provider3",
+                    },
+                ]
+            },
+        )
+
+        self.assertEqual(200, channel.code, msg=channel.json_body)
+        self.assertEqual("@user:test", channel.json_body["name"])
+        self.assertEqual(2, len(channel.json_body["external_ids"]))
+        self.assertEqual(
+            channel.json_body["external_ids"],
+            [
+                {"auth_provider": "auth_provider2", "external_id": "external_id2"},
+                {"auth_provider": "auth_provider3", "external_id": "external_id3"},
+            ],
+        )
+        self._check_fields(channel.json_body)
+
+        # Get user
+        channel = self.make_request(
+            "GET",
+            self.url_other_user,
+            access_token=self.admin_user_tok,
+        )
+
+        self.assertEqual(200, channel.code, msg=channel.json_body)
+        self.assertEqual("@user:test", channel.json_body["name"])
+        self.assertEqual(
+            channel.json_body["external_ids"],
+            [
+                {"auth_provider": "auth_provider2", "external_id": "external_id2"},
+                {"auth_provider": "auth_provider3", "external_id": "external_id3"},
+            ],
+        )
+        self._check_fields(channel.json_body)
+
+        # Remove external_ids
+        channel = self.make_request(
+            "PUT",
+            self.url_other_user,
+            access_token=self.admin_user_tok,
+            content={"external_ids": []},
+        )
+        self.assertEqual(200, channel.code, msg=channel.json_body)
+        self.assertEqual("@user:test", channel.json_body["name"])
+        self.assertEqual(0, len(channel.json_body["external_ids"]))
+
     def test_deactivate_user(self):
         """
         Test deactivating another user.