A device (1) for packaging a product shaped as a set of cigarettes in a corresponding container (A), defining a package for housing the product, comprises means (11) for forming the container (A) and appropriate means (21, 21) to dispense a corresponding adhesive (B1, B2) for joining corresponding panels of the container. Said appropriate means (21) to dispense a corresponding adhesive are provided next to the exit from the forming means (11) and are movable with respect to said container (A).