A 7'1" (2.17 m) center born in Munich, West Germany, Bagarić had averaged 18.3 points and 10.4 rebounds per game for the Croatian team Benston Zagreb before the Bulls selected him with the 24th pick in the 2000 NBA draft.

He returned to Europe after the Bulls bought out his contract in 2003, and began playing for the Greek club Olympiacos.

In September 2012, he signed a one-month deal with Sporting Al Riyadi Beirut in Lebanon.

In the 2013–14 season, he played for Étoile Sportive du Sahel in Tunisia, KK Zabok in Croatia and Al-Ahli Benghazi in Libya.

[7] With the junior national teams of Croatia, Bagarić won the gold medal at the 1996 FIBA Europe Under-18 Championship.