Born in Calasparra, Region of Murcia, Vélez graduated in Labour Relations and Human Resources from the University of Murcia. He then became a member of the management board at the Murcian Health Service.[2]
Vélez was voted onto his hometown's council in 1999. In October 2014, he was elected mayor after the resignation of Jesús Navarro due to poor approval ratings.[3] He renewed his mandate in 2015 and 2019, and resigned in February 2020 when named the Government Delegate for the region.[4]
In November 2021, Vélez was voted secretary general of the Socialist Party of the Region of Murcia (PSRM) with 2,867 votes, compared to 567 for former regional minister Lourdes Retuerto.[5]