An apparatus for feeding packaging machines with stacks of cutouts includes a centering member for supporting members of a plurality of stacks of cutouts, the stacks being arranged mutually side by side so as to form parallel and mutually adjacent rows on the supporting members; a unit for removing and transferring individual rows, provided with a head fitted with pushers which are arranged vertically side by side and are adapted to move a single row of stacks in a horizontal transfer direction; a switching platform which is adapted to cooperate with the pushers so as to receive the row of stacks and allow its transfer to a belt for input to the packaging machine.