An electrostatic cleaner (1) for eliminating polluting particulate material suspended in air or in a gaseous fluid comprises an elimination chamber (3) with an inlet (4) and an outlet (5), means (6) for generating a gaseous flow through the elimination chamber, means (7) for electrostatically charging the polluting particulate material at the inlet of the chamber, at least one pair of opposite electrodes (10, 11; 12, 13) with a different electric potential in order to collect the polluting particulate material on at least one of the electrodes (12). Means are provided for the continuous or discontinuous removal of the polluting particulate material deposited on one or more of the collecting electrodes (12).