Cut turkey into 2 1/2-inch strips. Place in a heavy-duty zip-top plastic bag. Add taco seasoning; seal and shake to coat.
Place turkey, celery, and onion in a 2 1/2-quart slow cooker. Stir in tomato and green chiles. Cover and cook at HIGH 4 hours. Stir in cheese.
Warm tortillas. Spoon turkey mixture in center of each tortilla; roll up. Serve with desired toppings.