diff --git a/changes/3342.bugfix.rst b/changes/3342.bugfix.rst
new file mode 100644
index 0000000000..cd5cb86728
--- /dev/null
+++ b/changes/3342.bugfix.rst
@@ -0,0 +1 @@
+An incompatibility with Textual 3.0 that caused log messages to be generated on the console on app exit has been resolved.
diff --git a/textual/pyproject.toml b/textual/pyproject.toml
index 1c922f4306..ef7297f7f3 100644
--- a/textual/pyproject.toml
+++ b/textual/pyproject.toml
@@ -66,7 +66,7 @@ root = ".."
 
 [tool.setuptools_dynamic_dependencies]
 dependencies = [
-    "textual >= 0.44.0",
+    "textual >= 3.0.0, < 4.0.0",
     "toga-core == {version}",
 ]
 
diff --git a/textual/src/toga_textual/app.py b/textual/src/toga_textual/app.py
index 6dfe60a2f0..571301004a 100644
--- a/textual/src/toga_textual/app.py
+++ b/textual/src/toga_textual/app.py
@@ -1,4 +1,5 @@
 import asyncio
+import threading
 
 import toga
 from textual.app import App as TextualApp
@@ -27,6 +28,7 @@ def __init__(self, interface):
         self.interface._impl = self
 
         self.loop = asyncio.new_event_loop()
+        asyncio.set_event_loop(self.loop)
         self.native = TogaApp(self)
 
         self._current_window = None
@@ -56,7 +58,21 @@ def exit(self):
         self.native.exit()
 
     def main_loop(self):
-        self.loop.run_until_complete(self.native.run_async(headless=self.headless))
+        # This is duplicating the bulk of TextualApp.run(); however, that entry point
+        # doesn't give any control over the event loop that is used. The key detail
+        # is that the _context() is required to capture logging messages generated
+        # as the app is shutting down. See textualize/textual#5091.
+        with self.native._context():
+            try:
+                self.native._loop = self.loop
+                self.native._thread_id = threading.get_ident()
+
+                self.loop.run_until_complete(
+                    self.native.run_async(headless=self.headless)
+                )
+            finally:
+                self.native._loop = None
+                self.native._thread_id = 0
 
     def set_icon(self, icon):
         pass