His career began at Čukarički, having played for Red Star Belgrade as a youth.
His performances at Čukarički caught the eye of Dynamo Kyiv manager Valeriy Lobanovskyi and the Ukrainian club purchased him in January 2001.
After six months without club, he signed a one-year contract with Partizan on 17 January 2009.
[2] In September 2010, he announced his retirement from professional football due to the prolonged problems with injuries.
[3] Gavrančić was part of the Serbia and Montenegro national team's "Famous Four" defence, alongside Mladen Krstajić, Ivica Dragutinović and Nemanja Vidić, that conceded just one goal during the ten 2006 FIFA World Cup qualification matches, setting a new record for the fewest goals conceded.