Bunjevčević joined Tottenham Hotspur in May 2001 from Red Star Belgrade for a reported fee of £5 million.

[3] In September of the 2001–02 season Tottenham played Chelsea in the league and Bunjevčević suffered a fractured cheekbone which left him out of the squad till December.

[2][4] Starting only in League Cup matches, during the 2004–05 season he scored his only goals (two) for the club (in the 6–0 away defeat of Oldham Athletic on 22 September in the competition,[5] and a late equaliser in the 4–3 away win against Bolton Wanderers on 29 October that took the game into extra time).

[7] At the beginning of March 2008 he was named as Red Star Belgrade's sporting director, replacing Stevan Stojanović in the position.

[10] In May 2016, Bunjevčević was elected into an executive board of the Football Association of Serbia under a new president, Slaviša Kokeza.