Dice the chicken breast into 1/2-inch pieces and place into a large mixing bowl. Add spinach, tomatoes, ricotta, mozzarella, pepper and salt, and mix thoroughly.
Arrange precooked pasta sheets on a cutting board and place two or three rounded tablespoons of filling mixture down the center of each pasta sheet and carefully roll pasta around filling in a cigar fashion.
Place the rolled cannelloni, side by side, into an ovenproof shallow baking dish. Place Alfredo sauce and tomato sauce in bowl and mix until well incorporated. Pour sauce over cannelloni covering completely. Sprinkle grated Parmesan cheese over top of sauce. Cover with aluminum foil.
Bake at 350°F for approximately 20 minutes. Remove foil and continue to bake for an additional 20 minutes, or until an internal temperature of 165°F is reached. Remove from oven and serve family style or on individual plates garnished with fresh diced tomatoes, and basil or Italian parsley.