Preheat your oven to 350°F (175°C).
Bring a large pot of salted water to a boil. Add the spaghetti and cook according to package instructions until al dente. Drain and set aside.
In a medium saucepan, heat the olive oil over medium heat. Add the diced onion, bell pepper, and garlic, and cook until softened (about 5 minutes).
In a large mixing bowl, combine the cooked chicken, cream of mushroom soup, cream of chicken soup, chicken broth, diced tomatoes, and cooked vegetables. Stir until well combined.
Fold in the cooked spaghetti and mix until the pasta is evenly coated.
Pour the mixture into a greased 9x13-inch baking dish. Sprinkle the grated cheddar cheese on top.
Bake in the preheated oven for 30 minutes, or until heated through and the cheese is bubbly and slightly golden.
Remove from the oven and let it cool for a few minutes before serving.