The device makes two coupling structures (11, 12) of the apparatus (1) interact sequentially with a mobile chassis (19) carried by a machine (2). The primary structure (11) reaches a docking state simply as a result of the progress of the machine (2) on the ground (6) towards the apparatus (1). At this stage, there is still a large distance between the engaging hooking means (16 and 17) of the secondary structure (12). In order to bring them together, the driver of the machine (2) orders the lifting of the mobile chassis (19). This lifts the apparatus (1) and makes it pivot about the axis (31) defined by the primary hooking structure (11), until the secondary structure (12) is in turn coupled. A spring (27) then tensions the two structures (11, 12) relative to each other, completing the rigid securing of the frame (9) of the device (1) to the mobile chassis (19). The invention also relates to the use of the device for fully automatic coupling-decoupling regardless of random variables such as uneven ground, the height of the chassis of the machine and fouling of the coupling means.