diff --git a/CHANGES.rst b/CHANGES.rst
index 34695123..22e22218 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -28,6 +28,9 @@ Unreleased
     the endpoint name. :issue:`4041`
 -   Combine URL prefixes when nesting blueprints that were created with
     a ``url_prefix`` value. :issue:`4037`
+-   Roll back a change to the order that URL matching was done. The
+    URL is again matched after the session is loaded, so the session is
+    available in custom URL converters. :issue:`4053`
 
 
 Version 2.0.0
diff --git a/src/flask/ctx.py b/src/flask/ctx.py
index 065edd5f..5c064635 100644
--- a/src/flask/ctx.py
+++ b/src/flask/ctx.py
@@ -395,9 +395,6 @@ class RequestContext:
 
         _request_ctx_stack.push(self)
 
-        if self.url_adapter is not None:
-            self.match_request()
-
         # Open the session at the moment that the request context is available.
         # This allows a custom open_session method to use the request context.
         # Only open a new session if this is the first time the request was
@@ -409,6 +406,11 @@ class RequestContext:
             if self.session is None:
                 self.session = session_interface.make_null_session(self.app)
 
+        # Match the request URL after loading the session, so that the
+        # session is available in custom URL converters.
+        if self.url_adapter is not None:
+            self.match_request()
+
     def pop(self, exc: t.Optional[BaseException] = _sentinel) -> None:  # type: ignore
         """Pops the request context and unbinds it by doing that.  This will
         also trigger the execution of functions registered by the
diff --git a/tests/test_converters.py b/tests/test_converters.py
index 14c92afd..d94a7658 100644
--- a/tests/test_converters.py
+++ b/tests/test_converters.py
@@ -1,6 +1,7 @@
 from werkzeug.routing import BaseConverter
 
-from flask import has_request_context
+from flask import request
+from flask import session
 from flask import url_for
 
 
@@ -28,12 +29,13 @@ def test_custom_converters(app, client):
 def test_context_available(app, client):
     class ContextConverter(BaseConverter):
         def to_python(self, value):
-            assert has_request_context()
+            assert request is not None
+            assert session is not None
             return value
 
     app.url_map.converters["ctx"] = ContextConverter
 
-    @app.route("/<ctx:name>")
+    @app.get("/<ctx:name>")
     def index(name):
         return name
 
diff --git a/tests/test_session_interface.py b/tests/test_session_interface.py
index aa9ecafa..39562f5a 100644
--- a/tests/test_session_interface.py
+++ b/tests/test_session_interface.py
@@ -2,21 +2,26 @@ import flask
 from flask.sessions import SessionInterface
 
 
-def test_open_session_endpoint_not_none():
-    # Define a session interface that breaks if request.endpoint is None
+def test_open_session_with_endpoint():
+    """If request.endpoint (or other URL matching behavior) is needed
+    while loading the session, RequestContext.match_request() can be
+    called manually.
+    """
+
     class MySessionInterface(SessionInterface):
-        def save_session(self):
+        def save_session(self, app, session, response):
             pass
 
-        def open_session(self, _, request):
+        def open_session(self, app, request):
+            flask._request_ctx_stack.top.match_request()
             assert request.endpoint is not None
 
-    def index():
-        return "Hello World!"
-
-    # Confirm a 200 response, indicating that request.endpoint was NOT None
     app = flask.Flask(__name__)
-    app.route("/")(index)
     app.session_interface = MySessionInterface()
-    response = app.test_client().open("/")
+
+    @app.get("/")
+    def index():
+        return "Hello, World!"
+
+    response = app.test_client().get("/")
     assert response.status_code == 200