Preheat oven to 350°F. Grease a 9x13-inch baking dish.
Cook spaghetti according to package directions until al dente. Drain and set aside.
In a large skillet, melt butter over medium heat. Add onion, bell pepper, and garlic. Sauté 5 minutes until vegetables are softened.
In a large bowl, combine cream of mushroom soup, cream of chicken soup, chicken broth, and sour cream. Whisk until smooth.
Add shredded chicken, sautéed vegetables, salt, pepper, and paprika to the soup mixture. Stir to combine.
Add cooked spaghetti to the mixture and toss until pasta is evenly coated with sauce.
Transfer spaghetti mixture to prepared baking dish, spreading evenly.
Sprinkle cheddar and mozzarella cheeses over the top.
Bake 25-30 minutes until cheese is melted and bubbly. If cheese browns too quickly, cover with foil.
Let rest 5 minutes before serving.
