At the end of his first professional season, Jedvaj was targeted and approached by Italian club Roma, although the initial offer was rejected by the Dinamo board. On 10 July 2013, however, it was confirmed that Jedvaj had signed a contract with the Roman club. Jedvaj made his Roma debut on 1 December 2013, coming on as an 83rd-minute substitute in a 4–0 Serie A victory over Genoa. He made his starting debut for the club against the same opposition in the last round of the Serie A season, with Genoa winning the clash 1–0 at the Stadio Luigi Ferraris. Those were Jedvaj's only two appearances for the season, appearing on the bench 33 times for Roma in the 2013–14 season.