A device for fastening a headrest to a backrest of a vehicle seat comprises first and second guide units for receiving first and second headrest columns. First and second receiving units fixed on the backrest receive sleeve-like portions of the first and second guide units. The second guide unit comprises a locking mechanism for locking various vertical positions of the second headrest column relative to the second guide unit. At least one rib is arranged on an outer lateral surface of each sleeve-like portion. At least one recess, in which the rib of the respective guide unit engages in a positive locking manner, is arranged on each receiving unit. A width of the rib of the first guide unit is greater than a width of the recess of the second receiving unit.