The machine comprises an unwinding section (3) for unwinding parent reels (Ba, Bb) of web material (Na, Nb), and at least one unwinding station (15). A winding device (41, 53) is arranged in the unwinding station, and a longitudinal strip (S) of web material is fed to it and a respective spool (B) of web material is formed in it. A control unit (70) is also provided, configured to control the winding speed of the longitudinal strip (S) in the winding station (15), so as to perform an acceleration cycle to accelerate the winding of the longitudinal strip (S), comprising at least one step of gradually increasing the feeding speed (Vp) of the longitudinal strip (S), wherein the feeding speed is linked to the diameter of the spool (B).