An apparatus for the transverse welding of a tape traveling in a machine direction, comprising: a stationary structure, a rotary structure rotatable with respect to the stationary structure about a rotation axis perpendicular to said machine direction, a plurality of welding units carried by said rotary structure and spaced apart in a circumferential direction, wherein each of said welding units comprises an inner welding element fixed relative to the rotary structure and an outer welding element cyclically movable with respect to the rotary structure between a release position and an operative position, and vice versa, wherein each of said outer welding elements during the movement from said release position to said operative position, and vice versa, performs an angular rotation movement about a respective radial axis perpendicular to said rotation axis, and a linear translation movement along said radial axis.