Born in Salzburg, Kuljić started his professional career in Salzburg but made his name at Austrian Football First League side SV Pasching with whom he won promotion to the Austrian Football Bundesliga in 2002. He repeated that feat with SV Ried in 2005, when he also became 2nd division top goalscorer. In 2006, he became league top goalscorer[2] and subsequently moved abroad to join Swiss side FC Sion but controversially[3] returned to Austria after one year when he signed for Vienna club Austria Wien.
He made his debut for the Austria national team in an August 2005 friendly match against Scotland and has earned 20 caps, scoring three goals. He became a regular in the national team squad but was surprisingly overlooked for Euro 2008.[5]
Extortion
In November 2013, Kuljić was taken in custody after former Kapfenberger teammate Dominique Taboga claimed he was blackmailed by Kuljić to manipulate match results.[6] After being accused of trying to manipulate 18 matches in the first two Austrian tiers, Kuljić was sentenced to five years in prison in autumn 2014.[7] He was released early in March 2017 for good conduct.[7]
Drug dealing
In September 2019 Kuljić was arrested for drug dealing. In December he was handed a one-year prison sentence with Kuljić stating that he had only been involved with drug dealing because of a cocaine addiction he was suffering from.[7]