Career
Božić started his career at Zrinjski Mostar of Premier League of Bosnia and Herzegovina. In summer 2000, he moved to Zuid-West-Vlaanderen of Belgian League. He went to Šibenik in summer 2002, due to the merge of Zuid-West-Vlaanderen and K.S.V. Ingelmunster.
Božić back to Belgian League in summer 2006 for Beveren, but the relegation he made his Belgian career with another early education
After 1 season in Rijeka he returned to Šibenik in the Croatian First League. On 22 July 2014, Božić transferred to China League One side Beijing Baxy.