An apparatus includes a piece-supporting plane to support one or more worked pieces, and first and second gripping devices, respectively defining first and second gripping planes of a worked piece. The apparatus moves the first and the second gripping devices among: a picking position wherein the first or the second gripping device is configured to pick up a worked piece laid on the piece-supporting plane; an exchange position wherein the first gripping device and the second gripping device are mutually oriented such that the first and the second gripping planes of the worked piece are facing each other to allow transferring the worked piece from the first gripping device to the second gripping device, or vice versa; and a laying position, wherein the second gripping device or the first gripping device is configured to release the worked piece being transferred in the exchange position in a piece storage area.