Combine cubed potatoes, ham, onion, carrots, celery, chicken broth, garlic powder, salt, and pepper in a 6-quart slow cooker.
Cover and cook on Low for 6 to 8 hours (or High for 3 to 4 hours) until the potatoes are fork-tender.
In a small saucepan over medium heat, melt the butter and whisk in the flour, cooking for 1 minute to remove the raw flour taste.
Gradually whisk the whole milk into the butter-flour mixture until smooth and slightly thickened.
Pour the milk mixture into the slow cooker and stir thoroughly to combine with the broth and vegetables.
Cover and cook on High for an additional 20 to 30 minutes until the soup has thickened to a creamy consistency.