Bring a large pot of salted water to a gentle boil. Add tortellini and cook according to package directions until tender. Drain and set aside.
Season chicken cubes with Cajun seasoning, salt, and pepper.
In a large skillet over medium-high heat, melt butter. Add seasoned chicken and cook until golden brown and cooked through, about 5–7 minutes. Remove chicken and set aside.
Reduce heat to medium. Add minced garlic to the skillet and sauté until fragrant, about 30 seconds.
Pour in milk while whisking constantly. Add Velveeta and cream cheese cubes. Stir until the cheeses melt and the sauce is smooth.
Stir in shredded mozzarella and Parmesan cheese. Continue whisking until the sauce is creamy and thickened. Adjust seasoning with Cajun seasoning, salt, or pepper as needed.
Return cooked chicken and tortellini to the skillet. Gently toss to coat evenly with the creamy sauce.
Serve hot, garnished with chopped fresh parsley.