diff --git a/src/agents/voice/models/openai_stt.py b/src/agents/voice/models/openai_stt.py
index 7ac0084281..ff03256775 100644
--- a/src/agents/voice/models/openai_stt.py
+++ b/src/agents/voice/models/openai_stt.py
@@ -321,18 +321,51 @@ def _check_errors(self) -> None:
             if exc and isinstance(exc, Exception):
                 self._stored_exception = exc
 
-    def _cleanup_tasks(self) -> None:
-        if self._listener_task and not self._listener_task.done():
-            self._listener_task.cancel()
+    async def _cleanup_tasks(self) -> None:
+        current_task = asyncio.current_task()
+        tasks_to_await: set[asyncio.Task[Any]] = set()
 
-        if self._process_events_task and not self._process_events_task.done():
-            self._process_events_task.cancel()
+        while True:
+            while True:
+                tasks = [
+                    task
+                    for task in (
+                        self._listener_task,
+                        self._process_events_task,
+                        self._stream_audio_task,
+                        self._connection_task,
+                    )
+                    if task is not None and task is not current_task and task not in tasks_to_await
+                ]
+                if not tasks:
+                    break
+
+                for task in tasks:
+                    if not task.done():
+                        task.cancel()
+
+                tasks_to_await.update(tasks)
+                await asyncio.sleep(0)
 
-        if self._stream_audio_task and not self._stream_audio_task.done():
-            self._stream_audio_task.cancel()
+            if not tasks_to_await:
+                return
 
-        if self._connection_task and not self._connection_task.done():
-            self._connection_task.cancel()
+            for task in tasks_to_await:
+                if not task.done():
+                    task.cancel()
+
+            await asyncio.gather(*tasks_to_await, return_exceptions=True)
+
+            if all(
+                task is None or task is current_task or task in tasks_to_await
+                for task in (
+                    self._listener_task,
+                    self._process_events_task,
+                    self._stream_audio_task,
+                    self._connection_task,
+                )
+            ):
+                return
 
     async def transcribe_turns(self) -> AsyncIterator[str]:
         self._connection_task = asyncio.create_task(self._process_websocket_connection())
@@ -367,7 +400,7 @@ async def close(self) -> None:
         if self._websocket:
             await self._websocket.close()
 
-        self._cleanup_tasks()
+        await self._cleanup_tasks()
 
 
 class OpenAISTTModel(STTModel):
diff --git a/tests/voice/test_openai_stt.py b/tests/voice/test_openai_stt.py
index cd503c60f2..368ebff9bf 100644
--- a/tests/voice/test_openai_stt.py
+++ b/tests/voice/test_openai_stt.py
@@ -165,6 +165,42 @@ async def test_stream_audio_sends_correct_json():
     await session.close()
 
 
+@pytest.mark.asyncio
+async def test_close_awaits_cancelled_background_tasks():
+    input_audio = await FakeStreamedAudioInput.get(count=0)
+    stt_settings = STTModelSettings()
+    session = OpenAISTTTranscriptionSession(
+        input=input_audio,
+        client=AsyncMock(api_key="FAKE_KEY"),
+        model="whisper-1",
+        settings=stt_settings,
+        trace_include_sensitive_data=False,
+        trace_include_sensitive_audio_data=False,
+    )
+
+    cleanup_events = [asyncio.Event() for _ in range(4)]
+
+    async def wait_until_cancelled(cleanup_event: asyncio.Event) -> None:
+        try:
+            await asyncio.Event().wait()
+        finally:
+            cleanup_event.set()
+
+    tasks = [asyncio.create_task(wait_until_cancelled(event)) for event in cleanup_events]
+    (
+        session._listener_task,
+        session._process_events_task,
+        session._stream_audio_task,
+        session._connection_task,
+    ) = tasks
+
+    await asyncio.sleep(0)
+    await session.close()
+
+    assert all(task.done() for task in tasks)
+    assert all(event.is_set() for event in cleanup_events)
+
+
 @pytest.mark.asyncio
 @pytest.mark.parametrize(
     "created,updated,completed",