diff --git a/synapse/storage/events.py b/synapse/storage/events.py
index 5d56ceeab..3104815f1 100644
--- a/synapse/storage/events.py
+++ b/synapse/storage/events.py
@@ -1397,12 +1397,8 @@ class EventsStore(
                 self._simple_update_txn(
                     txn,
                     table="redactions",
-                    keyvalues={
-                        "redacts": event.event_id,
-                    },
-                    updatevalues={
-                        "have_censored": False,
-                    }
+                    keyvalues={"redacts": event.event_id},
+                    updatevalues={"have_censored": False},
                 )
 
     def _store_rejected_events_txn(self, txn, events_and_contexts):
@@ -1568,9 +1564,15 @@ class EventsStore(
     def _store_redaction(self, txn, event):
         # invalidate the cache for the redacted event
         txn.call_after(self._invalidate_get_event_cache, event.redacts)
-        txn.execute(
-            "INSERT INTO redactions (event_id, redacts) VALUES (?,?)",
-            (event.event_id, event.redacts),
+
+        self._simple_insert_txn(
+            txn,
+            table="redactions",
+            values={
+                "event_id": event.event_id,
+                "redacts": event.redacts,
+                "received_ts": self._clock.time_msec(),
+            },
         )
 
     @defer.inlineCallbacks
diff --git a/synapse/storage/events_bg_updates.py b/synapse/storage/events_bg_updates.py
index 6587f31e2..5717baf48 100644
--- a/synapse/storage/events_bg_updates.py
+++ b/synapse/storage/events_bg_updates.py
@@ -67,6 +67,10 @@ class EventsBackgroundUpdatesStore(BackgroundUpdateStore):
             self.DELETE_SOFT_FAILED_EXTREMITIES, self._cleanup_extremities_bg_update
         )
 
+        self.register_background_update_handler(
+            "redactions_received_ts", self._redactions_received_ts
+        )
+
     @defer.inlineCallbacks
     def _background_reindex_fields_sender(self, progress, batch_size):
         target_min_stream_id = progress["target_min_stream_id_inclusive"]
@@ -397,3 +401,60 @@ class EventsBackgroundUpdatesStore(BackgroundUpdateStore):
             )
 
         return num_handled
+
+    @defer.inlineCallbacks
+    def _redactions_received_ts(self, progress, batch_size):
+        """Handles filling out the `received_ts` column in redactions.
+        """
+        last_event_id = progress.get("last_event_id", "")
+
+        def _redactions_received_ts_txn(txn):
+            # Fetch the set of event IDs that we want to update
+            sql = """
+                SELECT event_id FROM redactions
+                WHERE event_id > ?
+                ORDER BY event_id ASC
+                LIMIT ?
+            """
+
+            txn.execute(sql, (last_event_id, batch_size))
+
+            rows = txn.fetchall()
+            if not rows:
+                return 0
+
+            upper_event_id, = rows[-1]
+
+            # Update the redactions with the received_ts.
+            #
+            # Note: Not all events have an associated received_ts, so we
+            # fallback to using origin_server_ts. If we for some reason don't
+            # have an origin_server_ts, lets just use the current timestamp.
+            #
+            # We don't want to leave it null, as then we'll never try and
+            # censor those redactions.
+            sql = """
+                UPDATE redactions
+                SET received_ts = (
+                    SELECT COALESCE(received_ts, origin_server_ts, ?) FROM events
+                    WHERE events.event_id = redactions.event_id
+                )
+                WHERE ? <= event_id AND event_id <= ?
+            """
+
+            txn.execute(sql, (self._clock.time_msec(), last_event_id, upper_event_id))
+
+            self._background_update_progress_txn(
+                txn, "redactions_received_ts", {"last_event_id": upper_event_id}
+            )
+
+            return len(rows)
+
+        count = yield self.runInteraction(
+            "_redactions_received_ts", _redactions_received_ts_txn
+        )
+
+        if not count:
+            yield self._end_background_update("redactions_received_ts")
+
+        return count
diff --git a/synapse/storage/schema/delta/56/redaction_censor2.sql b/synapse/storage/schema/delta/56/redaction_censor2.sql
new file mode 100644
index 000000000..77a5eca49
--- /dev/null
+++ b/synapse/storage/schema/delta/56/redaction_censor2.sql
@@ -0,0 +1,20 @@
+/* Copyright 2019 The Matrix.org Foundation C.I.C.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+ALTER TABLE redactions ADD COLUMN received_ts BIGINT;
+CREATE INDEX redactions_have_censored_ts ON redactions(received_ts) WHERE not have_censored;
+
+INSERT INTO background_updates (update_name, progress_json) VALUES
+  ('redactions_received_ts', '{}');