In 2007, Osman signed a youth team contract with Anadolu Efes after his outstanding performance at KK Bosna.

He was loaned for the 2011–12 season to the Pertevniyal of the Turkish Basketball First League, which was at the time the farm team of Anadolu Efes.

In the summer of 2012, Osman signed a professional contract with the Anadolu Efes senior team.

The Cavaliers made it to the 2018 NBA Finals, but lost 4–0 to the Golden State Warriors.

Four days later, Osman was named a participant for the 2019 Rising Stars Challenge as a member of the World Team.

[10] On 7 September 2024 Osman signed a one-year deal with the reigning EuroLeague and Greek League champions Panathinaikos.