Mix in a bowl the garlic, sugar, paprika, salt, pepper, celery salt, onion salt and olive oil, add the wings to this mixture, mix until all wings are covered with the seasoning.
Put the seasoned wings into a covered bowl, or large freezer bag, and place in the refrigerator. Allow the wings to marinate in the refrigerator for at least two hours, up to 24 hours.
While the grill is heating, remove the wings from the refrigerator and place onto a cooking sheet. Pat the wings dry with paper towels. Drying the wings before grilling will allow for a crispier skin that better approximates the texture of a deep-fried wing.