Born in Strumica, Socialist Republic of Macedonia, Socialist Federal Republic of Yugoslavia, Paunović made his professional debut at only 17 with FK Partizan.
The following summer he moved to Spain, where he would stay for most of the following decade playing for a host of clubs, starting in the 1995–96 season with modest CA Marbella and reaching the 1998–99 UEFA Cup Winners' Cup final with RCD Mallorca (with whom he scored five league goals in that campaign, to help the Balearic Islands team finish third), as well as having three separate stints with Atlético Madrid.

Paunović had his best year in 2002–03 with CD Tenerife in Segunda División, netting 18 times in 38 appearances although the insular side could only rank eighth.
After a return to Atlético and a brief stay in Germany with Hannover 96, he joined Getafe CF for 2005–06's top flight, enjoying his finest season in La Liga by scoring ten goals in 30 league matches to help the Madrid outskirts club to the ninth place; due to the years spent in the country, he received a Spanish passport in 2006.

Paunović was signed by Russian Premier League's FC Rubin Kazan in March 2007, after falling out of favour with Getafe coach Bernd Schuster.
The following year, he agreed a two and a half year deal with UD Almería in January.
His debut was a sour one, playing 20 minutes off the bench against Racing de Santander in a 0–1 away defeat, while also receiving two yellow cards in one minute (with the consequent dismissal); he would score on two occasions towards the season's end, in a 2–4 away defeat against former team Getafe and in the last matchday, a 3–1 victory at RCD Espanyol.

On 12 July 2008, it was announced that Paunović signed a two-year deal with his former club Partizan.
On 13 August he scored in a 2–2 draw with Turkey's Fenerbahçe SK, in a UEFA Champions League qualifying round.
On 24 December however, he announced his decision to retire from the game.

On 29 June 2009, Paunović went on trial with the New York Red Bulls, but eventually turned down the one-year contract offer.
In June 2011, after nearly three years out of football, the 33-year-old signed a deal with another North American club, Philadelphia Union, after a trial stint.
He scored his first goal with his new team late in the month, in a 3–2 win against Chivas USA.

On 19 January 2012, Paunović officially announced his retirement for the second time.
Born in Strumica, Socialist Republic of Macedonia, Socialist Federal Republic of Yugoslavia, Paunović made his professional debut at only 17 with FK Partizan. The following summer he moved to Spain, where he would stay for most of the following decade playing for a host of clubs, starting in the 1995–96 season with modest CA Marbella and reaching the 1998–99 UEFA Cup Winners' Cup final with RCD Mallorca (with whom he scored five league goals in that campaign, to help the Balearic Islands team finish third), as well as having three separate stints with Atlético Madrid.
Paunović had his best year in 2002–03 with CD Tenerife in Segunda División, netting 18 times in 38 appearances although the insular side could only rank eighth. After a return to Atlético and a brief stay in Germany with Hannover 96, he joined Getafe CF for 2005–06's top flight, enjoying his finest season in La Liga by scoring ten goals in 30 league matches to help the Madrid outskirts club to the ninth place; due to the years spent in the country, he received a Spanish passport in 2006.
Paunović was signed by Russian Premier League's FC Rubin Kazan in March 2007, after falling out of favour with Getafe coach Bernd Schuster. The following year, he agreed a two and a half year deal with UD Almería in January. His debut was a sour one, playing 20 minutes off the bench against Racing de Santander in a 0–1 away defeat, while also receiving two yellow cards in one minute (with the consequent dismissal); he would score on two occasions towards the season's end, in a 2–4 away defeat against former team Getafe and in the last matchday, a 3–1 victory at RCD Espanyol.
On 12 July 2008, it was announced that Paunović signed a two-year deal with his former club Partizan. On 13 August he scored in a 2–2 draw with Turkey's Fenerbahçe SK, in a UEFA Champions League qualifying round. On 24 December however, he announced his decision to retire from the game.
On 29 June 2009, Paunović went on trial with the New York Red Bulls, but eventually turned down the one-year contract offer. In June 2011, after nearly three years out of football, the 33-year-old signed a deal with another North American club, Philadelphia Union, after a trial stint. He scored his first goal with his new team late in the month, in a 3–2 win against Chivas USA.
On 19 January 2012, Paunović officially announced his retirement for the second time.
Veljko Paunović