diff --git a/sentry_sdk/integrations/tornado.py b/sentry_sdk/integrations/tornado.py
index 7eb36f81d4..1dc495ad45 100644
--- a/sentry_sdk/integrations/tornado.py
+++ b/sentry_sdk/integrations/tornado.py
@@ -1,5 +1,6 @@
 import sys
 import weakref
+from inspect import iscoroutinefunction
 
 from sentry_sdk.hub import Hub, _should_send_default_pii
 from sentry_sdk.utils import (
@@ -42,20 +43,38 @@ def setup_once():
 
         old_execute = RequestHandler._execute
 
-        @coroutine
-        def sentry_execute_request_handler(self, *args, **kwargs):
-            hub = Hub.current
-            integration = hub.get_integration(TornadoIntegration)
-            if integration is None:
-                return old_execute(self, *args, **kwargs)
-
-            weak_handler = weakref.ref(self)
-
-            with Hub(hub) as hub:
-                with hub.configure_scope() as scope:
-                    scope.add_event_processor(_make_event_processor(weak_handler))
-                result = yield from old_execute(self, *args, **kwargs)
-                return result
+        awaitable = iscoroutinefunction(old_execute)
+
+        if awaitable:
+            # Starting Tornado 6 RequestHandler._execute method is a standard Python coroutine (async/await)
+            # In that case our method should be a coroutine function too
+            async def sentry_execute_request_handler(self, *args, **kwargs):
+                hub = Hub.current
+                integration = hub.get_integration(TornadoIntegration)
+                if integration is None:
+                    return await old_execute(self, *args, **kwargs)
+
+                weak_handler = weakref.ref(self)
+
+                with Hub(hub) as hub:
+                    with hub.configure_scope() as scope:
+                        scope.add_event_processor(_make_event_processor(weak_handler))
+                    return await old_execute(self, *args, **kwargs)
+        else:
+            @coroutine
+            def sentry_execute_request_handler(self, *args, **kwargs):
+                hub = Hub.current
+                integration = hub.get_integration(TornadoIntegration)
+                if integration is None:
+                    return old_execute(self, *args, **kwargs)
+
+                weak_handler = weakref.ref(self)
+
+                with Hub(hub) as hub:
+                    with hub.configure_scope() as scope:
+                        scope.add_event_processor(_make_event_processor(weak_handler))
+                    result = yield from old_execute(self, *args, **kwargs)
+                    return result
 
         RequestHandler._execute = sentry_execute_request_handler
 
diff --git a/tox.ini b/tox.ini
index 0139dffa4f..bd4407e794 100644
--- a/tox.ini
+++ b/tox.ini
@@ -34,7 +34,7 @@ envlist =
     {pypy,py2.7,py3.5,py3.6,py3.7,py3.8}-rq-0.12
 
     py3.7-aiohttp
-    {py3.7,py3.8}-tornado
+    {py3.7,py3.8}-tornado-{5,6}
 
 [testenv]
 deps =
@@ -90,7 +90,8 @@ deps =
     aiohttp: aiohttp>=3.4.0,<3.5.0
     aiohttp: pytest-aiohttp
 
-    tornado: tornado>=5,<6
+    tornado-5: tornado>=5,<6
+    tornado-6: tornado>=6.0a1
 
     linters: black
     linters: flake8