diff --git a/asgiref/wsgi.py b/asgiref/wsgi.py
index 40fba205..8fbb4a7d 100644
--- a/asgiref/wsgi.py
+++ b/asgiref/wsgi.py
@@ -63,6 +63,7 @@ def build_environ(self, scope, body):
             "wsgi.version": (1, 0),
             "wsgi.url_scheme": scope.get("scheme", "http"),
             "wsgi.input": body,
+            "wsgi.input_terminated": True,  # https://gist.github.com/mitsuhiko/5721547
             "wsgi.errors": BytesIO(),
             "wsgi.multithread": True,
             "wsgi.multiprocess": True,
diff --git a/tests/test_wsgi.py b/tests/test_wsgi.py
index aabea4df..27c732b2 100644
--- a/tests/test_wsgi.py
+++ b/tests/test_wsgi.py
@@ -256,7 +256,8 @@ def wsgi_application(environ, start_response):
 
 
 @pytest.mark.asyncio
-async def test_wsgi_multi_body():
+@pytest.mark.parametrize("has_content_length", [True, False])
+async def test_wsgi_multi_body(has_content_length):
     """
     Verify that multiple http.request events with body parts are all delivered
     to the WSGI application.
@@ -264,7 +265,14 @@ async def test_wsgi_multi_body():
 
     def wsgi_application(environ, start_response):
         infp = environ["wsgi.input"]
-        body = infp.read(12)
+        if has_content_length:
+            # this wsgi application reads the content length header and operates on that
+            body = infp.read(12)
+        else:
+            # this wsgi application supports [wsgi.input_terminated](https://gist.github.com/mitsuhiko/5721547)
+            # and reads until EOF.
+            assert environ["wsgi.input_terminated"]
+            body = infp.read()
         assert body == b"Hello World!"
         start_response("200 OK", [])
         return []