Preheat the oven to 375°F (190°C). Grease a 9x13-inch baking dish with cooking spray or olive oil.
In a large skillet, heat the olive oil over medium heat. Add the diced chicken, garlic powder, onion powder, oregano, salt, and pepper. Cook until the chicken is browned and cooked through, about 6-8 minutes.
In a large bowl, combine the cooked rice and the cooked chicken mixture. Mix well to combine.
In a separate bowl, prepare the tzatziki sauce by mixing the Greek yogurt, grated cucumber, lemon juice, dill, salt, and pepper. Stir until well combined.
Add half of the tzatziki sauce to the rice and chicken mixture, and mix until evenly coated.
Transfer the rice and chicken mixture to the prepared baking dish. Spread it out evenly.
Pour the remaining tzatziki sauce over the top of the rice mixture. Sprinkle with mozzarella and feta cheese.
Bake in the preheated oven for 25-30 minutes, or until the cheese is melted and bubbly.
Remove from the oven and let it cool for a few minutes. Garnish with fresh parsley if desired before serving.