He signed his first professional contract with the club on 14 August 2013, alongside Miladin Stevanović, penning a three-year deal.

They were both promoted back to Partizan in the 2015–16 campaign, with Bogosavac playing regularly under manager Ivan Tomić in the second half of the season.

On 14 February 2020, he joined Russian Premier League club Akhmat Grozny on loan until the end of the 2019–20 season, with an option to purchase.

[3] On 3 July 2020, Akhmat activated their purchase option and signed a four-year contract with Bogosavac.

He made his debut for Serbia national football team on 20 March 2019 in a friendly against Germany, as a starter.