Combine hash browns, ham, onion, celery, chicken broth, salt, pepper, and garlic powder in a slow cooker. Stir well to combine. Place the lid on the slow cooker.
Cook on Low heat until celery is soft, 4 to 5 hours.
Mix in cream cheese and Cheddar cheese. Stir until cheese is melted. Cover and cook on Low for an additional 30 minutes, stirring occasionally. Serve topped with chopped green onions as a garnish.