In an internal-combustion engine equipped with an electronically controlled hydraulic system for variable actuation of the intake valves (7), an operating step of refilling prior to ignition of the engine is activated in order to refill a pressure chamber (C) of the system with fluid when, after a prolonged inactivity of the engine, the aforesaid chamber has been emptied. In this refilling operating step, the supply of fuel to the engine is inhibited, and the camshaft (11) of the engine is driven in rotation following upon activation of the engine-starting electrical machine (53). In this way, a pumping member (16) associated to the tappet (15) for actuating an intake valve (7) is used as pump for drawing fluid into the pressure chamber (C) from an auxiliary fluid tank (600). During this step, an electrically actuated control valve (24) is opened and closed in synchronism with the movement of the pumping member (16) so as to be open when the pumping member (16) advances towards the pressure chamber (C) and be instead closed when the pumping member (16) moves away from the pressure chamber (C).