Spray the slow cooker with nonstick cooking spray.
Place the chicken breasts in the slow cooker, then add the drained artichoke hearts, undrained diced tomatoes with peppers, and the diced onion on top.
Cover and cook on high for 4 hours (or on low for 6 hours) until the chicken is cooked through and tender.
Remove the lid, add the diced Cheddar, grated Parmesan, and heavy cream to the slow cooker, then replace the lid until the cheeses have melted.
Stir the chicken and sauce until well combined, shredding or chopping the chicken as desired.
Stir in the cooked pasta until evenly coated with the sauce, then serve warm.
