The first Jesuit school in Arequipa was founded in 1578 under the name Colegio de Santiago but was soon closed by Viceroy Francisco de Toledo, who opposed the school.
He did his primary schooling at the Colegio San José in Arequipa, followed by secondary education at Colegios de la Independencia Nacional (Arequipa) and Colegio Nuestra Señora de Guadalupe (Lima).
As a private architect he produced the designs for the residences of Secundino Lozana (El Cortijo) in Barranquitas and Dionisio Trigo in Santurce, the General Electric store in San Juan, Colegio San José in Río Piedras and the Casino de Puerto Rico in El Condado.
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After receiving his early education there at the "Escuela San Vicente and San José," (Colegio San José) he decided to study law at the Universidad Nacional de San Agustín de Arequipa, and later transferred to finish his studies at the National University of San Marcos in Lima.
Vélez began playing soccer at an early age in Puerto Rico with Colegio San Jose, but moved to Nick Bollettieri's IMG Soccer Academy when in high school.