A rewinding machine is described including: a path for feeding the web material towards a winding system; interruption members to interrupt the web material at the end of winding of a log; a core insertion channel, defined by a rolling surface and a movable member; a core feeder to insert winding cores in succession in the channel; an electrostatic device positioned along the channel to electrostatically charge the winding cores and/or the web material thus causing, due to the electrostatic charges, reciprocal adhesion of the core and initial free edge of the web material obtained by interruption of the material at the end of winding of each log.