Place the chicken breasts in the bottom of the slow cooker.
Add the chopped artichoke hearts, squeezed spinach, cream cheese cubes, minced garlic, salt, and pepper on top of the chicken.
Cover and cook on low for 4 to 5 hours, until the chicken reaches an internal temperature of 165 degrees.
Shred the chicken directly in the slow cooker using two forks, then stir everything together until the cream cheese melts into a smooth sauce.
Sprinkle the mozzarella and Parmesan cheeses over the top, cover again, and cook for 15 more minutes until the cheese melts.