A two-time All-EuroLeague selection, he won the EuroLeague championship with Panathinaikos, in 2007.

Vujanić started his professional career with Crvena zvezda (Red Star Belgrade), in 1999.

After two seasons at the club, he signed with Partizan Belgrade, in the summer of 2001.

In the summer of 2003, he moved to the Italian League, and signed a three-year deal with Skipper Bologna.

With the senior FR Yugoslav national team, Vujanić won the gold medal at the 2002 FIBA World Championship, in Indianapolis.