The apparatus for feeding packaging machines with stacks of sheet material includes a trolley-like support provided with a vertically arranged rotatable belt having orthogonally connected thereto a plurality of pairs of support walls which define an accommodation seat for respective stacks of material in sheets, and a unit for removing and transferring the stacks which has a head provided with an element for gripping a stack. The head is movable vertically, laterally and horizontally so as to arrange itself at a selected accommodation seat in order to remove a stack therefrom and subsequently move it to a station for feeding the material in sheets to the packaging machine. The pairs of support walls are relatively mutually displaceable along a horizontal axis to thereby support a stack in a closed position and release a stack, or alternatively to receive a stack, in an open position.