Born in Požarevac on the eve of World War II to parents hailing from Montenegro — tax office clerk Živojin Vasović and homemaker Jelka Laušević — young Velibor was the couple's ninth child. He had four older brothers and three older sisters while another one of his sisters died before he was born. With the Nazi German invasion and subsequent dismemberment of the Yugoslav kingdom in April 1941, Vasović's father got taken prisoner by the Germans, spending four years in captivity, while his oldest siblings joined the Partisan resistance movement.