Mix together flour, salt, and pepper in a shallow bowl. Dredge steak pieces in flour mixture to lightly coat.

Heat oil in a large skillet over medium heat. Cook and stir celery, onion, and carrots in hot oil until tender, about 5 minutes. Add coated steak pieces; cook and stir until lightly browned, about 5 minutes more.

Transfer steak-vegetable mixture to the slow cooker. Stir in tomatoes with juice, brown sugar, and Worcestershire sauce.

Cover and cook on Low until steak is very tender, 8 to 10 hours.