diff --git a/gql/transport/requests.py b/gql/transport/requests.py
index 4e4e6ffb..996e6909 100644
--- a/gql/transport/requests.py
+++ b/gql/transport/requests.py
@@ -123,6 +123,9 @@ def connect(self):
             # Creating a session that can later be re-use to configure custom mechanisms
             self.session = requests.Session()
 
+            if self.headers:
+                self.session.headers.update(self.headers)
+
             # If we specified some retries, we provide a predefined retry-logic
             if self.retries > 0:
                 adapter = HTTPAdapter(
diff --git a/tests/test_aiohttp.py b/tests/test_aiohttp.py
index 00bd8a0f..7ba9b3ec 100644
--- a/tests/test_aiohttp.py
+++ b/tests/test_aiohttp.py
@@ -1918,3 +1918,25 @@ async def handler(request):
             await session.execute("qmlsdkfj")
 
         assert "request should be a GraphQLRequest object" in str(exc_info.value)
+
+
+@pytest.mark.asyncio
+async def test_aiohttp_save_headers_in_session():
+    """Regression test for issue #613"""
+    from gql.transport.aiohttp import AIOHTTPTransport
+
+    transport = AIOHTTPTransport("url", headers={"test": "header"})
+    await transport.connect()
+    assert transport.session
+    assert transport.session.headers["test"] == "header"
+
+    transport2 = AIOHTTPTransport("url")
+    await transport2.connect()
+    assert transport2.session
+
+    del transport.session.headers["test"]
+
+    assert transport.session.headers == transport2.session.headers
+
+    await transport.close()
+    await transport2.close()
diff --git a/tests/test_requests.py b/tests/test_requests.py
index 7de4a12a..4cb8fb10 100644
--- a/tests/test_requests.py
+++ b/tests/test_requests.py
@@ -1272,3 +1272,24 @@ def test_code():
             assert pi == Decimal("3.141592653589793238462643383279502884197")
 
     await run_sync_test(server, test_code)
+
+
+def test_requests_save_headers_in_session():
+    """Regression test for issue #613"""
+    from gql.transport.requests import RequestsHTTPTransport
+
+    transport = RequestsHTTPTransport("url", headers={"test": "header"})
+    transport.connect()
+    assert transport.session
+    assert transport.session.headers["test"] == "header"
+
+    transport2 = RequestsHTTPTransport("url")
+    transport2.connect()
+    assert transport2.session
+
+    del transport.session.headers["test"]
+
+    assert transport.session.headers == transport2.session.headers
+
+    transport.close()
+    transport2.close()