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, Argentine-born Juan Antonio Flecha raced for Spain, and Alejandro Borrajo only achieved a third place, also at the Giro.

In October 2015, after spending 11 seasons riding professionally for Italian teams, Belgian squad Etixx–Quick-Step announced that Richeze would join them from 2016 on a two-year contract, with a role as a lead-out man for Marcel Kittel and Fernando Gaviria.

Before the start of the 2008 Giro d'Italia Richeze tested positive for a steroid named stanozolol which resulted in his expulsion from the race.

Despite being initially cleared by the Argentine Cycling Federation he was banned by the Court of Arbitration for Sport for two years.