Shifting device for an automatic vehicle transmission

This device comprises a selector (14), articulated on a main support (16), and first (18) and second (20) guide means for this selector (14) according to, respectively, a first movement for selecting the operating configuration of the gearbox P, R, N, D and a second movement for changing gear. The first guide means (18) impose a rotational movement of the selector (14) around a first geometric axis of rotation (X). The second guide means (20) impose a tilting movement of the selector (14) around a second tilting axis (Y). Preferably, the first and second guide means (20) comprise a common member, forming a rocker (22), connected, on one hand, to the selector (14), by a pivot-type linkage materializing the axis of rotation (X) and, on the other hand, to the main support (16) by a pivot-type linkage materializing the tilting axis (Y).