A device for fastening gift bags or shopper-type bags comprising a length of adhesive tape (9) with a decorative object (2), fixed to one or both ends of the length of tape. Said device is produced in series by an apparatus comprising: actuators for linear and angular feed, a pair of pneumatic pincers (8, 8'), a cutter (10), a reel (11) to carry the roll of adhesive tape, a stitching device (12) and a dispenser of the decorative objects to be mounted on the tape. A microprocessor controls the apparatus for cyclical execution of the steps in a method in which: the princers engage the end of the tape through a cutter and pull the tape for a previously set length to bring it between the stitching device and a first pompom. The cutter then cuts the tape. The pompom (2) is stitched to the non-glued surface of the tape and the pincers pull the tape for an equal length so as to bring its other end between the stitching device and a second pompon which is then stitched onto the tape. The pincers rotate and open to expel the finished product.