Tobacco products are wrapped by a unit equipped with a rotating drum carrying a set of holder mechanisms around the periphery, each rotatable about an axis parallel to the axis of the drum, by which single products are supported and carried through an assembly station together with leaves of wrapping material received from a vacuum roller turning on an axis parallel to the axis of the drum; the vacuum roller revolves tangentially to the drum at the assembly station and comprises a system by which each leaf is transferred to a gripper associated with the support mechanism. The transfer system is timed to operate in a situation of substantially zero relative peripheral velocity between the support mechanism and the vacuum roller.