Velázquez began his career in the youth divisions of Atlántida Sport Club. After scoring 45 goals in an under-15 tournament with the team, he joined Libertad in 2003. He scored his first professional goal with the team in his debut, 10 December 2005, against 12 de Octubre. In 2009, Velázquez was loaned to Rubio Ñu. There, he got the chance to play regularly and seized the opportunity by becoming the top scorer in the Paraguayan Primera División Apertura championship, with 16 goals in 20 games. After finishing top scorer, Argentine club River Plate tried to sign him in July. However, the transfer did not materialize because the club wanted him on loan at a price well below that set by the owner of Velázques transfer rights, Libertad. A few weeks later, the player rejected an offer from CSKA Sofia of Bulgaria. Then in August, River attempted to sign him again, and this time the talks came to be quite close to the deal. The press even confirmed the transfer, but eventually the clubs could not agree on the form of payment. Almost immediately came an offer of another Argentine team, San Lorenzo; though this time River reported that the transfer deadline was due and San Lorenzo had not registered the Paraguayan player. After various comings and goings, Velázquez's continued his career with Rubio Ñu. In the Torneo Clausura, he scored 10 goals in 19 games, totalling 26 in 39 during the 2009 season. Therefore, he was the season top scorer of the Paraguayan Primera División. After the season, his loan ended and he returned to Libertad. On 30 December 2010, Velázquez was announced as the new signing of San Lorenzo, of the Argentine Primera División. After good performances at Libertad, Velázquez has been linked to a move to Mexican side Deportivo Toluca where the Paraguayan international Edgar Benítez plays. Toluca´s coach, former Paraguayan international and Toluca striker José Saturnino Cardozo requested Velázquez along with Olimpia's Paraguayan international Richard Ortiz. Other teams looking to sign Velázquez are Brazilian teams Palmeiras and Atletico Paranaense as well as teams in France and Italy.
