An apparatus for forming a laminated product by positioning a veneer onto a substrate while on a moving conveyor, including an elongate conveyor having an infeed end, a downstream outfeed end and adapted for moving successive known lengths of substrates having an upper surface carrying an adhesive along a longitudinal axis from the infeed end to the outfeed end at a known rate. At least one veneer supply source is positioned in a known location laterally offset from the longitudinal axis of the conveyor for supplying successive lengths of veneer to be applied onto a top surface of the moving lengths of substrate. A related method of operating the apparatus is disclosed.