Velázquez started training at the age of only 15, being in charge of youth teams in his hometown of Salamanca. His first job as a senior came in 2004, with AD Peña Respuela in the regional leagues. Velázquez made his debut with the professionals in 2010–11, being appointed at Polideportivo Ejido in the third division. He was fired late into the season, with the Andalusians eventually finishing 14th. Velázquez then joined Villarreal CF's setup, first being in charge of the C-side. On 24 December 2011, as José Francisco Molina left the reserves for the main squad, he was appointed his successor, thus becoming the youngest person ever to coach a club in the second level, aged 30 years and two months. On 13 June 2012, following the Yellow Submarine's top-flight relegation – which meant the B's also had to drop down a level even though they finished in 12th position in division two – Velázquez was named first teammanager. On 13 January of the following year, following a 1–1 away draw against UD Almería, he was relieved of his duties. In the following years, Velázquez continued to work in the second tier, being relegated with Real Murcia even though the side finished in fourth position and qualified to the play-offs, and being sacked by Real Betis after only five months in charge. During roughly ten months and starting in December 2015, he was in charge of C.F. Os Belenenses in the Portuguese Primeira Liga. Velázquez returned to his country and its second division on 13 October 2016, signing with AD Alcorcón. He eventually managed to steer them out of the relegation zone and also ousted RCD Espanyol in the fourth round of the Copa del Rey, renewing his contract a two further years after the latter achievement. Velázquez left Alkor on 4 June 2018, after narrowly avoiding relegation. From June–November of the same year he was in charge of Udinese Calcio of the Italian Serie A, being dismissed after only two league wins. Velázquez returned to the Portuguese top flight in November 2019, being appointed at Vitória F.C. until the end of the season. He left by mutual consent the following 2 July, with the team three points above the relegation zone having not won any of the five games since the resumption of play following the COVID-19 break.
