Born on 3 October 1939, in Požarevac, on the eve of World War II, to parents hailing from Montenegro—tax office clerk Živojin Vasović and homemaker Jelena "Jelka" Laušević—young Velibor was the couple's ninth child.

[2] The youngster completed primary education in his hometown before moving to capital Belgrade along with his entire family courtesy of his maternal uncle David Laušević who in the meantime rose to high post with the Directorate for State Security (UDB).

[2] Simultaneous with starting gymnasium studies, Vasović got introduced to the game of football at FK Novi Beograd, a small local lower-league outfit.

In the summer of 1963, twenty-three-year-old Vasović was coming off another stellar season for Partizan in which he greatly contributed to the crno-beli winning their third consecutive league title.

Club president, JNA general Ilija Radaković [sr], immediately approved payment of the double amount Red Star gave me.

His first competitive match for Red Star on 1 September 1963 was also the grand opening of the club's still not fully finished grandiose new stadium Marakana as crveno-beli came from behind to beat NK Rijeka 2–1.

Over the winter break, another transfer saga involving Vasović ensued as Partizan club president Radaković was successful in persuading the player to come back for even more money than Red Star gave him.

After several months of sitting out, Vasović got instructed by the Partizan vice-president Čeda Džomba to try to get a meeting with the highest political authority in SR Serbia at the time, federal interior secretary Aleksandar Ranković, in order to finally resolve the situation.

The row started over the internal decision to relieve general-secretary Nenezić of his duties as a person in charge of finances, a move pushed through by president Radaković.

As the 1964–65 season began under new head coach Aleksandar Atanacković, Partizan led the league, but with each coming week the row in the managing board increasingly affected player relations.

By December 1964, ahead of the last league fixture before the winter break, two opposing camps clearly emerged within the team—one group supporting dissenting general-secretary Nenezić was led by Jusufi and also included Milan Galić, Radoslav Bečejac, Joakim Vislavski, and head coach Atanacković while the other group supporting president Radaković was led by Vasović with Vladica Kovačević, Zoran Miladinović, and several youth players.

The dissenting group even resorted to initiating a mutiny, refusing to travel to Skopje for the final match of the first half of the season versus FK Vardar.

The very next day after the Skopje debacle, head coach Atanacković was relieved of his duties as the two factions prepared for the final showdown at the club's general assembly scheduled for January 1965 at the University of Belgrade's Faculty of Law.

Once Tito caught whiff of this, he acted swiftly, ordering action against each officer from the club's management board involved in the row by having them reassigned to another location.

On 10 October 2000, five days after the overthrow of Milošević's regime in Serbia, Vasović and about a dozen bodyguards broke into the FSJ offices at Terazije square in downtown Belgrade.