diff --git a/synapse/handlers/auth.py b/synapse/handlers/auth.py
index 4f881a439a..18cd2b62f0 100644
--- a/synapse/handlers/auth.py
+++ b/synapse/handlers/auth.py
@@ -263,10 +263,6 @@ class AuthHandler(BaseHandler):
         # authenticating for an operation to occur on their account.
         self._sso_auth_confirm_template = hs.config.sso_auth_confirm_template
 
-        # The following template is shown after a successful user interactive
-        # authentication session. It tells the user they can close the window.
-        self._sso_auth_success_template = hs.config.sso_auth_success_template
-
         # The following template is shown during the SSO authentication process if
         # the account is deactivated.
         self._sso_account_deactivated_template = (
@@ -1394,27 +1390,6 @@ class AuthHandler(BaseHandler):
             description=session.description, redirect_url=redirect_url,
         )
 
-    async def complete_sso_ui_auth(
-        self, registered_user_id: str, session_id: str, request: Request,
-    ):
-        """Having figured out a mxid for this user, complete the HTTP request
-
-        Args:
-            registered_user_id: The registered user ID to complete SSO login for.
-            session_id: The ID of the user-interactive auth session.
-            request: The request to complete.
-        """
-        # Mark the stage of the authentication as successful.
-        # Save the user who authenticated with SSO, this will be used to ensure
-        # that the account be modified is also the person who logged in.
-        await self.store.mark_ui_auth_stage_complete(
-            session_id, LoginType.SSO, registered_user_id
-        )
-
-        # Render the HTML and return.
-        html = self._sso_auth_success_template
-        respond_with_html(request, 200, html)
-
     async def complete_sso_login(
         self,
         registered_user_id: str,
diff --git a/synapse/handlers/sso.py b/synapse/handlers/sso.py
index 69ffc9d9c2..dcc85e9871 100644
--- a/synapse/handlers/sso.py
+++ b/synapse/handlers/sso.py
@@ -22,6 +22,7 @@ from typing_extensions import NoReturn, Protocol
 
 from twisted.web.http import Request
 
+from synapse.api.constants import LoginType
 from synapse.api.errors import Codes, RedirectException, SynapseError
 from synapse.handlers.ui_auth import UIAuthSessionDataConstants
 from synapse.http import get_request_user_agent
@@ -147,9 +148,13 @@ class SsoHandler:
         self._store = hs.get_datastore()
         self._server_name = hs.hostname
         self._registration_handler = hs.get_registration_handler()
+        self._auth_handler = hs.get_auth_handler()
         self._error_template = hs.config.sso_error_template
         self._bad_user_template = hs.config.sso_auth_bad_user_template
-        self._auth_handler = hs.get_auth_handler()
+
+        # The following template is shown after a successful user interactive
+        # authentication session. It tells the user they can close the window.
+        self._sso_auth_success_template = hs.config.sso_auth_success_template
 
         # a lock on the mappings
         self._mapping_lock = Linearizer(name="sso_user_mapping", clock=hs.get_clock())
@@ -598,9 +603,14 @@ class SsoHandler:
             )
         else:
             # success!
-            await self._auth_handler.complete_sso_ui_auth(
-                user_id, ui_auth_session_id, request
+            # Mark the stage of the authentication as successful.
+            await self._store.mark_ui_auth_stage_complete(
+                ui_auth_session_id, LoginType.SSO, user_id
             )
+
+            # Render the HTML confirmation page and return.
+            html = self._sso_auth_success_template
+            respond_with_html(request, 200, html)
             return
 
         # the user_id didn't match: mark the stage of the authentication as unsuccessful