Navarro was born in Salamanca. Having been one of Alberto Contador's domestiques for most of his career, he left Saxo Bank–Tinkoff Bank at the end of the 2012 season, and joined Cofidis on a two-year contract from the 2013 season onwards. In 2013, Navarro won the Vuelta a Murcia. He later had his first top ten grand tour finish, finishing 9th overall in the 2013 Tour de France. He had to abandon the 2014 Tour de France due to some intense stomach pain. At the 2014 Vuelta a España, he obtained the biggest victory of his career on Stage 13, a medium-mountain stage. He went on to finish 10th overall that year.