Bring a large pot of salted water to a boil. Add potatoes and cook until tender but still firm, about 15 minutes.
Drain, cool, peel, and chop potatoes.
While potatoes cook, place eggs in a saucepan and cover with cold water. Bring water to a boil; cover, remove from heat, and let eggs stand in hot water for 10 to 12 minutes.
Remove from hot water, cool, peel, and chop eggs.
Combine the potatoes, eggs, celery, onion, relish, mayonnaise, mustard, garlic salt, celery salt, and pepper in a large bowl. Mix together well and refrigerate until chilled.