Career
Ostojić spent five years playing for Sloboda Čačak at the start of his career. After his departure from Sloboda he spent time playing for several other third level clubs. He joined Javor Ivanjica in 2011 and played in the Serbian SuperLiga.
In June 14, 2013 the Greek superleague side Veria signed Branko on a free transfer.
Branko scored his first goal for the club in season 2013-2014 with an amazing shot against Skoda Xanthi, during the 31st matchday of the season. Despite being in Veria only for a season, Branko was named as the third club captain during the 2014-2015 season.
Ostojić renewed his contract with Veria for one more year on 21 May 2015.
