diff --git a/synapse/storage/background_updates.py b/synapse/storage/background_updates.py
index e5f0668f0..3fc25cd82 100644
--- a/synapse/storage/background_updates.py
+++ b/synapse/storage/background_updates.py
@@ -140,7 +140,7 @@ class BackgroundUpdateStore(SQLBaseStore):
             "background_updates",
             keyvalues=None,
             retcol="1",
-            desc="check_background_updates",
+            desc="has_completed_background_updates",
         )
         if not updates:
             self._all_done = True
@@ -148,6 +148,29 @@ class BackgroundUpdateStore(SQLBaseStore):
 
         return False
 
+    async def has_completed_background_update(self, update_name):
+        """Check if the given background update has finished running.
+
+        Returns:
+            Deferred[bool]
+        """
+
+        if self._all_done:
+            return True
+
+        if update_name in self._background_update_queue:
+            return False
+
+        update_exists = await self._simple_select_one_onecol(
+            "background_updates",
+            keyvalues={"update_name": update_name},
+            retcol="1",
+            desc="has_completed_background_update",
+            allow_none=True,
+        )
+
+        return not update_exists
+
     @defer.inlineCallbacks
     def do_next_background_update(self, desired_duration_ms):
         """Does some amount of work on the next queued background update