A high voltage generator of the DAC-controlled type, has an input terminal connected to a first voltage reference and an output terminal providing an output voltage and comprises at least a voltage control circuit and a charge pump circuit inserted, in series to each other, between the input and output terminals of the high voltage generator, and an output regulator connected to the output terminal of the high voltage generator and comprising at least a digital-to-analog converter or DAC. The output regulator further comprises at least an additional current regulation portion connected to the output terminal of the high voltage generator through a first resistive element of the output regulator as well to an enabling terminal which provides an enabling signal, the additional current regulation portion being supplied by a second voltage reference having a voltage level higher than a voltage level of the first voltage reference.