Đedović started his career with KK Bosna, but FC Barcelona signed him when he was just 16 years old. He never got a real chance to play in Barcelona, and spent most of the time on loans in Cornellà, Obradoiro and with Virtus Roma.[1] After leaving Barcelona, he played for Galatasaray and Alba Berlin.
In July 2013 he signed for Bayern Munich.[2] In July 2014, it was announced that he signed a two-year extension with the team.[3] On July 11, 2016, Đedović agreed on a contract extension with Bayern until 2018, including a team option for the 2018–19 season.[4]
He was one of the key players of Bosnia and Herzegovina national team. On EuroBasket 2011 he averaged 10.6 points, 5.2 rebounds and 4.2 assists per game,[6] while on EuroBasket 2013 he averaged 17.8 points, 5.2 rebounds and 4.2 assists per game.[7]
Đedović spent most of the first seven years of his life in Munich, Germany, due to the Bosnian War. Returning to Sarajevo in 1997, there was no infrastructure for him to continue playing football, but a basketball club opened in the city.[8] He is the older brother of Nedim Đedović. He has also held German citizenship since April 2015.[9]
Đedović has gained international attention for his physical resemblance to Swedish footballer Zlatan Ibrahimović, whose father was Bosnian.[10][11][12]