Preheat oven to 350°F (175°C) and lightly grease a 9x13 inch baking dish.
Bring a large pot of salted water to a boil. Cook spaghetti according to package directions until al dente, then drain.
In a medium skillet, melt butter over medium heat and sauté the diced onion and bell pepper until softened, approximately 5 minutes.
In a large heavy-bottomed pot over medium-low heat, combine the cream of mushroom soup, cream of chicken soup, Ro-Tel tomatoes (with liquid), and cubed processed cheese.
Stir the sauce mixture constantly until the cheese is completely melted and the texture is smooth.
Stir the shredded chicken and sautéed vegetables into the cheese sauce. Season with salt and black pepper.
Add the cooked spaghetti to the pot and toss thoroughly until the pasta is evenly coated with the sauce.
Transfer the mixture into the prepared baking dish and spread it into an even layer.
Bake for 30 minutes until the casserole is bubbling at the edges and heated through.
Remove from the oven and allow the dish to rest for 5 minutes before serving.