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 cheese for topping if desired.
Transfer the mixture to a slow cooker and spread it evenly.
Cover and cook on low for 2 to 3 hours, or until the dip is hot and bubbly. Stir occasionally to ensure even heating.
If using, sprinkle the reserved cheese on top during the last 15 minutes of cooking.
Once done, garnish with chopped green onions if desired. Serve warm with tortilla chips, celery sticks, or crackers.