A splicing device to join a first web material coming from a reel being fed (BA), to a second web material (NB), coming from a reel standing by (BB), comprising two heads (107A, 127A; 107B, 127B), each of which comprises: a roller (129A; 129B) associated with a clamping bar (143A, 145A; 143B, 145B) to hold an initial edge of the second web material (NB); a counter-pressure member (109A; 109B) cooperating with said roller (129A; 129B) to press said first and second web material (NA, NB) against each other; a cutting member (111A; 111B); a moving unit (113A; 113B), on which said counter-pressure member (109A; 109B) and said cutting member (111A; 111B) are carried. A first common control member (121) is provided to cause, by the movement it imparts to the moving unit of one or other head alternately: pinching of the first and second web material between the roller (129A; 129B) and the counter-pressure member (109A; 109B); cutting of the first web material; and release of the second web material.