A device, which connects a gearmotor to an aircraft wheel, comprising: a casing rotatably carrying a shaft driven by the gearmotor, the shaft having a fluted portion on which a gearwheel is mounted to slide along a longitudinal axis of the shaft without rotating relative to the shaft; a toothed ring for constraining to rotate with the aircraft wheel; and structure for moving the gearwheel axially between a retracted position (disengaged from the toothed ring) and an engaged position (gearwheel meshes with the toothed ring). The structure for moving the gearwheel comprises a hollow screw-and-nut assembly extending around the shaft. One element of the assembly is axially secured to the gearwheel but prevented from rotating by an anti-rotation member. The other element of the assembly is rotatably mounted inside the casing to be driven selectively by an electric motor so that rotating the electric motor causes the gearwheel to move axially.