Place potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, about 20 minutes. Drain, cool, peel, and chop.
Place eggs in a saucepan and cover with water. Bring to a boil, remove from heat, and let eggs stand in hot water for 15 minutes. Remove eggs from hot water, cool under cold running water, and peel. Discard yolks and chop whites.
Combine potatoes, egg whites, celery, onion, relish, mayonnaise, mustard, celery seed, garlic, and pepper in a large bowl. Mix together well and refrigerate until chilled.