As a coach, he had a successful spell in Budućnost in the 2006–07 season, when his team was leading in Montenegrin First League, but he resigned and joined Grbalj in February 2007, due to the disagreement with the board.[3] 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.
On 27 April 2010, Božović signed a three-year contract with FC Dynamo Moscow.[4]
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."[5]
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).[6]
In Serbia Božović was nicknamed Grof (the Count or Earl), because of his orderly and elegant appearance.[7]
On 29 May 2015 it was announced that Božović would manage his former club Red Star Belgrade.[10] His start as Red Star manager was turbulent. Red Star was eliminated by Kairat in the first qualifying round for the Europa League and started off the regular season with a comeback win against OFK Beograd and a draw against Metalac in Gornji Milanovac in the first two rounds of the Serbian Superliga. Serbian media and journalist were not on his side and criticized him and his team's play. After a draw against Radnički Niš in front of 22.000 fans who started to chant against the club board, Božović offered his resignation. Fans were explicit in their desire that board members must leave the club right away, not him, and gave clear support to Božović. Several board members including the vice president and the general director left the club and Božović started a "little war" with the media.[11] After the series of bad performances, Red Star dominated throughout the match and won after a comeback against Čukarički, considered the best match of the season.
Following these incidents, Božović masterminded Red Star to 24 straight wins in the regular season, a new club record, and dominated the Serbian Superliga with 32 points ahead of their rivals. With Božović at the helm Red Star made the best start in club history. Božović lead Red Star to the 27th club league title in history, and the first in his career. Božović stated that he is very happy like never before in his life.
2016-17
After clear and unambiguous support from Red Star fans, who were chanted his name and ask to stay, Grof Božović signed new two-year contract with Red Star to lead the club to the Champions League. Božović said that chants from the fans and whole stands of Marakana are the biggest thing which happened to him in his life, after birth of his sons. He record his first European victory, which is also Red Star first in three years and five matches in a row, against Valletta FC in first match of second qualifying round for the Champions League in Valletta.[12]
On 5 October 2018, he signed a 2-year contract with FC Krylia Sovetov Samara.[15] He left Krylia Sovetov by mutual consent on 28 June 2020, with the team in the last position in the table.[16]
As of 2023 – the record holder among foreign coaches in Russian Premier League in terms of the number of clubs led and seasons spent (7 and 11, respectively).[22]
The players who worked under him repeatedly noted his use of sex jokes in the training process.[22][23][24]
