The rewinding machine includes a first winding cradle, formed between a first winding roller, a second winding roller and a third winding roller, and a second winding cradle formed between the first winding roller, the second winding roller and a fourth winding roller. The first winding roller and the second winding roller define a nip through which nip the winding cores, around which the web material is found, pass and the web material is fed towards a roll being formed in the second winding cradle. A severing member is furthermore provided, acting on the web material between a winding core and the nip, to sever the web material thus generating a tail edge of a completed roll and a leading edge of a new roll to be wound.