The unwinder includes a pair of tailstocks adapted to engage and support a reel to be unwound and a peripheral unwinding device adapted to coact with a reel in the unwinding station. There is also provided a shuttle adapted to insert reels into the unwinding station, movable between a loading position of the reel on the shuttle and a position aligned with the pair of tailstocks, to transfer a reel from the shuttle to the tailstocks or vice versa. In use, the peripheral unwinding device is positioned under the reel of web material, so that the force exerted by the peripheral unwinding device on the reel being unwound has a component that is subtracted from the weight force of the reel.