diff --git a/flask/app.py b/flask/app.py
index fb791f33..9dfc3783 100644
--- a/flask/app.py
+++ b/flask/app.py
@@ -1484,8 +1484,10 @@ class Flask(_PackageBoundObject):
         Since a request context typically also manages an application
         context it would also be called when you pop a request context.
 
-        When a teardown function was called because of an exception it will
-        be passed an error object.
+        When a teardown function was called because of an unhandled exception
+        it will be passed an error object. If an :meth:`errorhandler` is
+        registered, it will handle the exception and the teardown will not
+        receive it.
 
         The return values of teardown functions are ignored.
 
diff --git a/tests/test_appctx.py b/tests/test_appctx.py
index 7ef7b479..fc2f6b13 100644
--- a/tests/test_appctx.py
+++ b/tests/test_appctx.py
@@ -81,7 +81,7 @@ def test_app_tearing_down_with_previous_exception(app):
     assert cleanup_stuff == [None]
 
 
-def test_app_tearing_down_with_handled_exception(app):
+def test_app_tearing_down_with_handled_exception_by_except_block(app):
     cleanup_stuff = []
 
     @app.teardown_appcontext
@@ -97,6 +97,49 @@ def test_app_tearing_down_with_handled_exception(app):
     assert cleanup_stuff == [None]
 
 
+def test_app_tearing_down_with_handled_exception_by_app_handler(app, client):
+    app.config['PROPAGATE_EXCEPTIONS'] = True
+    cleanup_stuff = []
+
+    @app.teardown_appcontext
+    def cleanup(exception):
+        cleanup_stuff.append(exception)
+
+    @app.route('/')
+    def index():
+        raise Exception('dummy')
+
+    @app.errorhandler(Exception)
+    def handler(f):
+        return flask.jsonify(str(f))
+
+    with app.app_context():
+        client.get('/')
+
+    assert cleanup_stuff == [None]
+
+
+def test_app_tearing_down_with_unhandled_exception(app, client):
+    app.config['PROPAGATE_EXCEPTIONS'] = True
+    cleanup_stuff = []
+
+    @app.teardown_appcontext
+    def cleanup(exception):
+        cleanup_stuff.append(exception)
+
+    @app.route('/')
+    def index():
+        raise Exception('dummy')
+
+    with pytest.raises(Exception):
+        with app.app_context():
+            client.get('/')
+
+    assert len(cleanup_stuff) == 1
+    assert isinstance(cleanup_stuff[0], Exception)
+    assert str(cleanup_stuff[0]) == 'dummy'
+
+
 def test_app_ctx_globals_methods(app, app_ctx):
     # get
     assert flask.g.get('foo') is None