Preheat the oven to 350 degrees F (175 degrees C).

Bring a large pot of lightly salted water to a boil. Cook spaghetti in the boiling water, stirring occasionally until tender yet firm to the bite, about 12 minutes. Drain; transfer to a large bowl.

Stir chicken, cream of mushroom soup, and cream of chicken soup into spaghetti; transfer to a 9x13-inch baking dish. Top with Cheddar cheese.

Bake in the preheated oven until cheese is melted and sauce is bubbly, about 30 minutes.