In a small bowl, whisk together mayonnaise, Greek yogurt, minced garlic, garlic powder, onion powder, salt, and pepper to create the garlic sauce.
Place shredded chicken in a large mixing bowl and toss with the garlic sauce until evenly coated.
Lay tortillas flat on a clean surface and distribute the chicken mixture evenly across the center of each.
Top the chicken with a blend of shredded cheddar and mozzarella cheese.
Fold the sides of the tortillas inward and roll tightly to form a wrap.
Heat olive oil in a large skillet over medium heat.
Place wraps seam-side down in the skillet and toast for 2-3 minutes per side until the tortilla is golden brown and the cheese is melted.
Remove from heat and serve immediately or wrap in foil for storage.