Career
After starting out with his local club Zabjelo, Božović joined Budućnost Podgorica in the 2004 winter transfer window. He was also loaned to Mladost Podgorica and Kom, before returning to the club and becoming the first-choice goalkeeper in the 2006-2007 season. On 14 January 2008, Božović was transferred to Partizan, on a four-year deal.
He then played the full 90 minutes in all of his team"s league fixtures in the 2008-2009 campaign, keeping a clean sheet in nine consecutive games, eventually being named in the competition"s best eleven.
In June 2010, Božović moved to Hungarian side Videoton, winning the league title in his debut season with the club On 23 June 2013, Božović joined Russian club Tom Tomsk on a free transfer.
He was the first-choice goalkeeper at the beginning of the 2013-2014 season, before losing his place in the starting lineup. In August 2014, Božović was loaned to Khimik Dzerzhinsk.
He returned to the Siberian club in December 2014, making one league appearance until the end of the 2014-2015 season.
Božović made his international debut for Montenegro in a 0–1 loss to Colombia at the Kirin Cup on 3 June 2007. He then served as a backup goalkeeper for Vukašin Poleksić during their unsuccessful qualification campaign for the 2010. Subsequently, Božović played the full 90 minutes in all of his team"s Union of European Football Associations Euro 2012 qualifying games, including a play-offs tie against the Czechoslovakian Republic.
However, Montenegro failed to reach the final tournament.