diff --git a/bigframes/exceptions.py b/bigframes/exceptions.py
index ef51f96575..1fb86d7bd6 100644
--- a/bigframes/exceptions.py
+++ b/bigframes/exceptions.py
@@ -30,7 +30,7 @@ class UnknownLocationWarning(Warning):
 
 
 class CleanupFailedWarning(Warning):
-    """Bigframes failed to clean up a table resource."""
+    """Bigframes failed to clean up a table or function resource."""
 
 
 class DefaultIndexWarning(Warning):
diff --git a/bigframes/session/anonymous_dataset.py b/bigframes/session/anonymous_dataset.py
index 3c1757806b..bdc6e7f59c 100644
--- a/bigframes/session/anonymous_dataset.py
+++ b/bigframes/session/anonymous_dataset.py
@@ -16,15 +16,21 @@
 import threading
 from typing import List, Optional, Sequence
 import uuid
+import warnings
 
+from google.api_core import retry as api_core_retry
 import google.cloud.bigquery as bigquery
 
 from bigframes import constants
 import bigframes.core.events
+import bigframes.exceptions as bfe
 from bigframes.session import temporary_storage
 import bigframes.session._io.bigquery as bf_io_bigquery
 
 _TEMP_TABLE_ID_FORMAT = "bqdf{date}_{session_id}_{random_id}"
+# UDFs older than this many days are considered stale and will be deleted
+# from the anonymous dataset before creating a new UDF.
+_UDF_CLEANUP_THRESHOLD_DAYS = 3
 
 
 class AnonymousDatasetManager(temporary_storage.TemporaryStorageManager):
@@ -137,8 +143,46 @@ def generate_unique_resource_id(self) -> bigquery.TableReference:
         )
         return self.dataset.table(table_id)
 
+    def _cleanup_old_udfs(self):
+        """Clean up old UDFs in the anonymous dataset."""
+        dataset = self.dataset
+        routines = list(self.bqclient.list_routines(dataset))
+        cleanup_cutoff_time = datetime.datetime.now(
+            datetime.timezone.utc
+        ) - datetime.timedelta(days=_UDF_CLEANUP_THRESHOLD_DAYS)
+
+        for routine in routines:
+            if (
+                routine.created < cleanup_cutoff_time
+                and routine._properties["routineType"] == "SCALAR_FUNCTION"
+            ):
+                try:
+                    self.bqclient.delete_routine(
+                        routine.reference,
+                        not_found_ok=True,
+                        retry=api_core_retry.Retry(timeout=0),
+                    )
+                except Exception as e:
+                    msg = bfe.format_message(
+                        f"Unable to clean this old UDF '{routine.reference}': {e}"
+                    )
+                    warnings.warn(msg, category=bfe.CleanupFailedWarning)
+
     def close(self):
         """Delete tables that were created with this session's session_id."""
         for table_ref in self._table_ids:
             self.bqclient.delete_table(table_ref, not_found_ok=True)
         self._table_ids.clear()
+
+        try:
+            # Before closing the session, attempt to clean up any uncollected,
+            # old Python UDFs residing in the anonymous dataset. These UDFs
+            # accumulate over time and can eventually exceed resource limits.
+            # See more from b/450913424.
+            self._cleanup_old_udfs()
+        except Exception as e:
+            # Log a warning on the failure, do not interrupt the workflow.
+            msg = bfe.format_message(
+                f"Failed to clean up the old Python UDFs before closing the session: {e}"
+            )
+            warnings.warn(msg, category=bfe.CleanupFailedWarning)
diff --git a/tests/system/large/test_session.py b/tests/system/large/test_session.py
index d28146498d..a525defe59 100644
--- a/tests/system/large/test_session.py
+++ b/tests/system/large/test_session.py
@@ -13,6 +13,7 @@
 # limitations under the License.
 
 import datetime
+from unittest import mock
 
 import google.cloud.bigquery as bigquery
 import google.cloud.exceptions
@@ -138,3 +139,35 @@ def test_clean_up_via_context_manager(session_creator):
         bqclient.delete_table(full_id_1)
     with pytest.raises(google.cloud.exceptions.NotFound):
         bqclient.delete_table(full_id_2)
+
+
+def test_cleanup_old_udfs(session: bigframes.Session):
+    routine_ref = session._anon_dataset_manager.dataset.routine("test_routine_cleanup")
+
+    # Create a dummy function to be deleted.
+    create_function_sql = f"""
+CREATE OR REPLACE FUNCTION `{routine_ref.project}.{routine_ref.dataset_id}.{routine_ref.routine_id}`(x INT64)
+RETURNS INT64 LANGUAGE python
+OPTIONS (entry_point='dummy_func', runtime_version='python-3.11')
+AS r'''
+def dummy_func(x):
+    return x + 1
+'''
+    """
+    session.bqclient.query(create_function_sql).result()
+
+    assert session.bqclient.get_routine(routine_ref) is not None
+
+    mock_routine = mock.MagicMock(spec=bigquery.Routine)
+    mock_routine.created = datetime.datetime.now(
+        datetime.timezone.utc
+    ) - datetime.timedelta(days=100)
+    mock_routine.reference = routine_ref
+    mock_routine._properties = {"routineType": "SCALAR_FUNCTION"}
+    routines = [mock_routine]
+
+    with mock.patch.object(session.bqclient, "list_routines", return_value=routines):
+        session._anon_dataset_manager._cleanup_old_udfs()
+
+    with pytest.raises(google.cloud.exceptions.NotFound):
+        session.bqclient.get_routine(routine_ref)
diff --git a/third_party/bigframes_vendored/pandas/core/frame.py b/third_party/bigframes_vendored/pandas/core/frame.py
index b434b51fb3..21bbbc2409 100644
--- a/third_party/bigframes_vendored/pandas/core/frame.py
+++ b/third_party/bigframes_vendored/pandas/core/frame.py
@@ -419,7 +419,7 @@ def to_gbq(
             >>> df = bpd.DataFrame({'col1': [1, 2], 'col2': [3, 4]})
             >>> destination = df.to_gbq(ordering_id="ordering_id")
             >>> # The table created can be read outside of the current session.
-            >>> bpd.close_session()  # Optional, to demonstrate a new session.
+            >>> bpd.close_session()  # Optional, to demonstrate a new session.  # doctest: +SKIP
             >>> bpd.read_gbq(destination, index_col="ordering_id")
                          col1  col2
             ordering_id