Živojinović (nicknamed Bata) was born in the village of Koraćica under the Kosmaj mountain near Mladenovac, at the time Kingdom of Yugoslavia (now Serbia).

A conflict between Dragoljub and the Chetniks during World War II forced the family to move to Belgrade.

Loitering around the "20th October" cinema, he watched AKUD Branko Krsmanović, a Belgrade troupe, through the window for several days until he was welcomed inside.

After graduating from acting schools in Niš and Novi Sad, he enrolled at the Drama Academy in Belgrade.

[4] On 4 July 2012 he suffered a severe stroke and was transported to a hospital specializing in cerebrovascular diseases called Sveti Sava in Belgrade.

[9][10] On 6 May 2016, after being transferred from Sveti Sava hospital to "KBC Dedinje", he was subject of an emergency surgery which, in order to stop his gangrene, resulted in a leg amputation.

[14] He was baptized as an infant in the Serbian Orthodox Church and despite his association with communism, remained a believer until the end of his life.

He won the award for Best Actor at the 11th Moscow International Film Festival in 1979 for his role in Moment.