A carcass sleeve (19) including at least one carcass ply and a pair of annular anchoring structures is fitted around a toroidal forming drum (30) arranged in a first radially contracted operational condition. The carcass sleeve (19) is toroidally shaped against at least one radially inner surface (43a) of an annular contrast element (43), while the forming drum (30) is positioned inside the carcass sleeve (19) and is concurrently expanded towards a second operational configuration. Upon reaching the second operational condition, the toroidally shaped carcass sleeve (19) is coupled to the forming drum (30). The forming drum (30), coupled to said carcass sleeve (19), is adapted to be transferred in the proximity of at least one application device of additional components (54) externally on said carcass sleeve (19).