Reclosable package of cigarettes, comprising: a group of cigarettes; a soft envelope having a parallelepiped shape and comprising a front surface, a rear surface, a top surface, a bottom surface and two side surfaces, the envelope encloses the group of cigarettes and is provided with a cigarette extraction opening; a stiffening element wrapping the envelope along at least two opposite surfaces of the envelope and at the extraction opening; a reclosable opening system consisting in an adhesive closing panel superimposed in a removable manner on an adhesive frame panel, the opening system covers the extraction opening; wherein the closing panel is movable between an opening position and a closing position of the extraction opening, and wherein the opening system is fastened to the stiffening element by firmly superimposing the frame panel on at least two opposite walls of the stiffening element and at the extraction opening.