Preheat the oven to 350°F.
Spray a 9x9-inch baking dish with nonstick cooking spray and set aside.
In a medium saucepan, add the cubed cream cheese, ranch dressing, buffalo sauce, black pepper, and garlic powder.
Cook over medium-low heat, whisking frequently, until the cream cheese has completely melted and the mixture is smooth and creamy.
Remove the saucepan from the heat.
Add the shredded chicken, 1/2 cup mozzarella cheese, and 1 1/2 cups cheddar cheese.
Stir until the chicken is evenly coated and the cheese is incorporated throughout the dip.
Transfer the buffalo chicken mixture to the prepared 9x9-inch baking dish and spread it into an even layer.
Sprinkle the remaining 1/2 cup mozzarella and 1/2 cup cheddar cheese evenly over the top.
Bake at 350°F for 20–30 minutes, or until the dip is hot and bubbling around the edges and the cheese on top has completely melted.
Set the oven to broil and broil the dip for approximately 2 minutes, or until the cheese on top is bubbly and golden brown.
Remove the buffalo chicken dip from the oven and garnish with chopped green onions.
Serve warm with tortilla chips, celery, carrots, crackers, or your favorite veggies.