A machine (1) includes an unwinding section (3) for unwinding parent reels (Ba, Bb) of web material (N), an unwinding section (3) for unwinding parent reels (Ba, Bb) of web material (Na, Nb), and at least one winding station (15). The winding station in turn includes a winding device (41, 51), to which a longitudinal strip (S) of web material is fed. In the winding station, a respective spool (B) of web material is formed. The winding station (15) further includes: a cutting device (81, 83) for the longitudinal strip (S), to cut the longitudinal strip (S) transversely, thus forming a tail edge, which remains on the spool (B) under formation, and a leading edge; and a holding device (85) for holding the leading edge of the longitudinal strip (S), to transfer the leading edge onto a tubular winding core (T) of a new spool to be wound.