Born in Lazarevo, a village near Zrenjanin, Bjeković started out at his local club Zadrugar Lazarevo, before switching to Proleter Zrenjanin. He stayed there for four years, making his Yugoslav First League debut in the 1967–68 season. In the summer of 1969, Bjeković was transferred to Partizan. He spent seven seasons with the club, scoring 82 league goals in 198 appearances for the Crno-beli. In the 1975–76 season, Bjeković was the Yugoslav First League top scorer with 24 goals, helping Partizan win its seventh championship title. In the summer of 1976, Bjeković moved abroad to France and signed with Nice. He played for the club over the next five seasons, scoring a total of 85 goals in 143 league appearances. In 2013, Bjeković was named the club's player of the century.
Bjeković started his managerial career in 1982 as an assistant to Miloš Milutinović at Partizan. He subsequently replaced Milutinović as manager at the start of the 1984–85 season. At the helm of Partizan, Bjeković won two consecutive league titles in 1986 and 1987. In 1987, Bjeković was appointed as manager by his former club Nice, but was released after two years. He again managed Partizan for two months in 1990. After his managerial career, Bjeković served as sporting director for Partizan for almost two decades. He resigned from the position in May 2007. By summer 2020, while holding a top-level position within the FSS, he gave an interview to Sportski žurnal in which he maximally minimized the archviements of the foreign players giving a prove of maximal loose impartial analisis. All 4 of Partizan foreigners that season archived their maximal goals, starting with Takuma Asano which recovered his place in the Japanese national team, going trough Seydouba Soumah who made his best season ever in Partizan being decicive in a number of games, then Bibras Natkho, Israeli national team captain, one of the best defensive midfieldes and playing organisers Partisan ever had lately, Bjekovic cosidered him "old", and, as last exemple, Umar Sadiq, a striker that menged an impressive Bjekovic miinimized it so much that didn´t even wanted to express what his real opinion about Sadiq is because otherwise it would even be suit to go into the media. It is a trend that it is usual with this persona from football that seems to think so low of Serbian players that regularly denegrates and votes for less foreigners becaause thinks that is the only way Serbian players can survive.
Personal life
His son, also named Nenad, played professional football for Marseille and Nantes, after starting out with Partizan.
