A device for positioning an off-shore platform (1) on a previously-installed support structure. Said platform has support piles (6) designed to rest on legs (4) of the support structure.The device includes means for bringing said support piles towards said legs which are provided with centering cones (5). Each pile is constituted by a tube containing a rod (13) associated with a damping unit (8). The lower portion of the rod (13) has a centering pin (16) and extends below the lower end of the pile in the damping unit rest position.