diff --git a/tornado/httpclient.py b/tornado/httpclient.py
index 3a45ffd04..488fe6de0 100644
--- a/tornado/httpclient.py
+++ b/tornado/httpclient.py
@@ -53,7 +53,7 @@
 from tornado.ioloop import IOLoop
 from tornado.util import Configurable
 
-from typing import Type, Any, Union, Dict, Callable, Optional, cast
+from typing import Type, Any, Union, Dict, Callable, Optional, Awaitable, cast
 
 
 class HTTPClient:
@@ -372,7 +372,9 @@ def __init__(
         user_agent: Optional[str] = None,
         use_gzip: Optional[bool] = None,
         network_interface: Optional[str] = None,
-        streaming_callback: Optional[Callable[[bytes], None]] = None,
+        streaming_callback: Optional[
+            Callable[[bytes], Optional[Awaitable[None]]]
+        ] = None,
         header_callback: Optional[Callable[[str], None]] = None,
         prepare_curl_callback: Optional[Callable[[Any], None]] = None,
         proxy_host: Optional[str] = None,
diff --git a/tornado/simple_httpclient.py b/tornado/simple_httpclient.py
index cc1637613..5ed273db3 100644
--- a/tornado/simple_httpclient.py
+++ b/tornado/simple_httpclient.py
@@ -33,7 +33,7 @@
 from io import BytesIO
 import urllib.parse
 
-from typing import Dict, Any, Callable, Optional, Type, Union
+from typing import Dict, Any, Callable, Optional, Type, Union, Awaitable
 from types import TracebackType
 import typing
 
@@ -687,14 +687,15 @@ def finish(self) -> None:
     def _on_end_request(self) -> None:
         self.stream.close()
 
-    def data_received(self, chunk: bytes) -> None:
+    def data_received(self, chunk: bytes) -> Optional[Awaitable[None]]:
         if self._should_follow_redirect():
             # We're going to follow a redirect so just discard the body.
-            return
+            return None
         if self.request.streaming_callback is not None:
-            self.request.streaming_callback(chunk)
+            return self.request.streaming_callback(chunk)
         else:
             self.chunks.append(chunk)
+            return None
 
 
 if __name__ == "__main__":
diff --git a/tornado/test/simple_httpclient_test.py b/tornado/test/simple_httpclient_test.py
index a40435e81..c1ee49c84 100644
--- a/tornado/test/simple_httpclient_test.py
+++ b/tornado/test/simple_httpclient_test.py
@@ -539,6 +539,26 @@ def test_streaming_follow_redirects(self):
         num_start_lines = len([h for h in headers if h.startswith("HTTP/")])
         self.assertEqual(num_start_lines, 1)
 
+    def test_streaming_callback_coroutine(self: typing.Any):
+        headers = []  # type: typing.List[str]
+        chunk_bytes = []  # type: typing.List[bytes]
+
+        @gen.coroutine
+        def _put_chunk(chunk):
+            chunk_bytes.append(chunk)
+            yield gen.moment
+
+        self.fetch(
+            "/hello",
+            header_callback=headers.append,
+            streaming_callback=_put_chunk,
+        )
+        chunks = list(map(to_unicode, chunk_bytes))
+        self.assertEqual(chunks, ["Hello world!"])
+        # Make sure we only got one set of headers.
+        num_start_lines = len([h for h in headers if h.startswith("HTTP/")])
+        self.assertEqual(num_start_lines, 1)
+
 
 class SimpleHTTPClientTestCase(AsyncHTTPTestCase, SimpleHTTPClientTestMixin):
     def setUp(self):