His father Svetozar "Toza" Živković was also a musician and a restaurant owner, while mother Budimka was a housewife.

He began working as a musician in the 1960s, first as an accordion player who accompanied other, more prominent singers, while later in the decade, he teamed up with other composers like Duško Radetić, Bane Popov, and Dušan Karaklajić, becoming a folk music star himself.

In the late 1990s and early 2000s he didn't record much, but he scored a few hits, like Danče, Ljubav je za sve godine and a duet with Lepa Lukić, and was again a co-host of the most popular music TV show in Serbia, Grand Show, on TV Pink.

He also held a very popular three-singers concert, performing with Predrag Cune Gojković and Miroslav Ilić.

Tozovac has two illegitimate sons, and stories continue to circulate that Živković loved many beauties, one of whom was Biljana Ristić.