Geldersmans finished fifth in 1962 in the final classification of the Tour de France as a teammate of winner Jacques Anquetil and wore the yellow jersey for two days. He also became Dutch champion in 1962 and won stages in the Tour of Spain and Paris-Nice.
In 1968, Geldermans was closely involved in the Tour de France of Jan Janssen as the team leader of the Dutch team in the Tour de France. That was the first of the two Dutch Tour victories.