Rodríguez was born in Barcelona, the son of an amateur rider in the 1960s, and later lived in Parets del Vallès. Some years later he moved to the Basque country to ride for Iberdrola, an amateur team associated to the professional cycling team ONCE-Eroski.
His nickname in the professional peloton is Purito, Spanish for little cigar, a name he was given in an early season training camp during his first year as a professional with ONCE-Eroski. When some of his teammates stepped up the pace in a small climb, he passed them making a hand gesture appearing to be smoking a cigar, suggesting he was climbing without much effort. The gesture was not welcomed by his teammates, who made him smoke a real cigar as a hazing ritual later in the evening
In 2010 he joined the Russian team Team Katusha, which guaranteed him a position at the Tour de France and a leading role in certain races throughout the season. Early in the season Rodríguez won the Volta a Catalunya, the UCI ProTour race held around Catalonia, and later won the Gran Premio Miguel Indurain and a stage at the Vuelta al País Vasco, where he eventually finished third. He also ended second behind Cadel Evans in the Flèche Wallonne. At the Tour de France he won the stage to Mende, which featured an uphill finish to the Côte de la Croix Neuve, with the finish line at the runway of the Mende Aerodrome. Rodríguez finished eight at the Tour de France. He continued his strong performance during the season with a fifth place at the Clásica de San Sebastián and a fourth place at the overall classification of the Vuelta a España, winning the stage to Peña Cabarga. Rodríguez topped the UCI World Ranking at the end of the season.