A device for programming PCM cells includes a pulse-generator circuit for supplying programming current pulses. The pulse-generator circuit includes: at least one first capacitive element; a charging circuit, connectable to the first capacitive element in a first operating condition, for bringing a reference voltage on the first capacitive element to a reset value; a discharge-current generator, selectively connectable to the first capacitive element in a second operating condition, for discharging the first capacitive element through a controlled discharge current; a logic unit, configured to control connection and disconnection of the first capacitive element), of the charging circuit, and of the discharge-current generator; and a voltage-to-current converter, for converting the reference voltage into current.