diff --git a/changelog.d/10326.bugfix b/changelog.d/10326.bugfix
new file mode 100644
index 000000000000..7ebda7cdc29c
--- /dev/null
+++ b/changelog.d/10326.bugfix
@@ -0,0 +1 @@
+Fix a long-standing bug where Synapse would return errors after 2<sup>31</sup> events were handled by the server.
diff --git a/synapse/storage/databases/main/events_bg_updates.py b/synapse/storage/databases/main/events_bg_updates.py
index 1c95c66648ca..29f33bac55bc 100644
--- a/synapse/storage/databases/main/events_bg_updates.py
+++ b/synapse/storage/databases/main/events_bg_updates.py
@@ -1146,6 +1146,16 @@ def process(txn: Cursor) -> None:
                 logger.info("completing stream_ordering migration: %s", sql)
                 txn.execute(sql)
 
+        # ANALYZE the new column to build stats on it, to encourage PostgreSQL to use the
+        # indexes on it.
+        # We need to pass execute a dummy function to handle the txn's result otherwise
+        # it tries to call fetchall() on it and fails because there's no result to fetch.
+        await self.db_pool.execute(
+            "background_analyze_new_stream_ordering_column",
+            lambda txn: None,
+            "ANALYZE events(stream_ordering2)",
+        )
+
         await self.db_pool.runInteraction(
             "_background_replace_stream_ordering_column", process
         )