In a large mixing bowl, combine the shredded chicken, softened cream cheese, buffalo sauce, and ranch dressing. Mix until well combined and smooth.
Stir in the shredded cheddar cheese and mozzarella cheese, reserving a little of each for topping if desired.
Transfer the mixture to a slow cooker and spread it evenly.
Cover and cook on low for 2-3 hours or until heated through and bubbly. Stir occasionally to ensure even heating.
If using, sprinkle the reserved cheese on top during the last 15 minutes of cooking.
Serve warm with tortilla chips, celery sticks, or crackers. Garnish with chopped green onions if desired.