Born in Užice, Radović passed all youth categories of the local club Sloboda.
[2] He started his senior career with Sloga Požega where he made 19 appearances in the Serbian League West.
[3] Playing for the club, he also scored his first senior goal in 3–1 away win against Sloga Petrovac na Mlavi on 21 April 2012.
[5] He made his debut for the club in 18 fixture match of the 2016–17 Serbian First League season, against Zemun.
[6] On February 14, 2024, Branko Radovic transferred to FK Jedinstvo Putevi Užice, where he currently plays.