Velez is a product of the famed River Plate youth academy having played in the same team as Erik Lamela and Roberto Pereyra, before leaving for another top-tier Argentinian team, Huracan, in search of first-team opportunities.
Huracán
Nicolás Vélez started his professional footballing career with Club Atlético Huracán at the age of 19.
After being released by his former club in Argentina, he joined Spanish 3rd tier club Atlético Sanluqueño. He left the club in 2013, saying there were “many problems” at the Spanish club, so he asked his agent to look at options elsewhere.
He signed for Warriors FC in the S.League in 2014. He scored a hat-trick for the Warriors against Albirex Niigata in a 4–0 victory, keeping them in contention of the title. In his first season in Singapore, he scored an impressive 21 goals in 26 appearances, second only to Brazilian Rodrigo Tosi helping Warriors FC to the S.League title. Velez capped his first Asian campaign by being named S.League young player of the year. In the 2015 Singapore Charity Shield which doubled as the first league game of the 2015 season, Vélez scored the only goal of the match, winning the Shield and the first three points of the season for the Warriors. He scored two goals in the next game, a 3–1 win over Harimau Muda. He notched his sixth goal of the season on 24 April 2015 against fellow title contenders Brunei DPMM FC before earning a red card in the 69th minute following an on-field spat. The South American also earned call-ups to Singapore Selection sides that took on Juventus, Arsenal and Stoke City in the last 18 months.
In August 2015 Velez announced that he has decided to join Indian Super League side NorthEast United. On his joining the Indian side he said "I'm very happy to have this chance, but I'm sad to leave Warriors, because I am leaving behind many friends in Singapore.I want to say 'thank you' to my club for giving me the chance to show what I can do alongside some of the best players in the world". After debuting on 6 October 2015 he scored his first goal on the same night in 82 minute with a losing effort against Kerala Blasters. He ended the season with 5 goals, marking his name as the top goal scorer for the club.
In January 2016, Vélez joined the Croatian First Football League club Hajduk Split and signed the contract with a two and half years. He made his debut on 13 February 2016 in a 2–0 win against Slaven Belupo. On 30 June 2016, he was released from Hajduk.
NorthEast United FC
In the third season of Indian Super League, Velez made his 2nd appearance for the club and assisted Katsumi Yusa for the first winning goal against Kerela Blasters on the night of October 1, 2016 when the season officially kick off. Velez was awarded the Hero of the Match in the 41st Match of the season between NorthEast United FC and Atlético de Kolkata.
Velez joined newly promoted side Negeri Sembilan for the 2018 Malaysian Super League season after leaving Suphanburi at the end of 2017. He scored his first goal when playing against fellow promoted side, Kuala Lumpur in a 2–0 home win.