As a coach he had a successful spell in Budućnost in 2006-2007 season, when his team was leading in Montenegrin First League, but he resigned in February 2007, due to the disagreement with the board. Božović also was successful in Borac Čačak, as he made a competitive team out of a humble club.
Russian side FC Amkar Perm qualified for the UEFA Europa League for the first time in club's history under his management. Next season, his new club FC Moscow was among the leaders in the Russian Premier League for long stretches, before fading in the end of the season and falling out of European qualification. In early 2010, FC Moscow dropped out of the Premier League due to financial considerations, and Božović became a free agent.
After the game against his former club, Amkar, he was questioned in the flash interview, did he feel that he was playing against the team he had built himself. His answer was: "I feel I was playing against players who made me a coach." 
He resigned from Dynamo on 21 April 2011 after losing in a Russian Cup quarterfinal against FC Rostov (winning the Cup was the last hope for Dynamo to qualify for UEFA Europa League).
In Serbia Božović was nicknamed Grof (the Count or Earl), because of his orderly and elegant appearance.