Disclosed is a system to be combined to one or more rewinding machines (1) for forming reels or logs of web material wound around winding mandrels. The system, whose function is to prepare the winding mandrels with the related winding cores positioned thereon, comprises in combination: a robot (5) for extracting winding mandrels (A) from formed reels (BB); a cutting unit (7) for cutting tubes (T) for forming tubular winding cores (AT) of settable axial length; an insertion unit (9), for introducing the winding mandrels into a set of tubular winding cores.