Born in
Sremska Mitrovica, Bogosavac joined the youth academy of
Partizan from Sirmium in 2008. He signed his first professional contract with the club on 14 August 2013, alongside
Miladin Stevanović, penning a three-year deal. In order to gain experience, the duo was immediately assigned to affiliated team
Teleoptik. 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. In February 2017, Bogosavac was transferred to
Čukarički on a three-year contract. He was selected in the
2017–18 Serbian SuperLiga Team of the Season due to his performances in the process. 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. On 3 July 2020, Akhmat activated their purchase option and signed a four-year contract with Bogosavac. ==International career==