Richeze was born in Bella Vista. In his first season as a professional racer, he obtained the second position in the last stage of the 2006 Giro d'Italia, finishing some centimetres behind Robert Förster. He is considered to be the Argentine cyclist to obtain the best result in any of the three main cycling tours (the "Giro d'Italia", the "Tour de France" and the "Vuelta a España"), since naturalised Lucien Petit-Breton raced for France, Argentina-born Juan Antonio Flecha raced for Spain, and Alejandro Borrajo only achieved a third place, also at the "Giro".