[1][2] Velázquez was born on 16 March 1803 in Zacualpan to Juan Felipe Velázquez de León, cousin of the scientist and lawyer, Joaquín Velázquez Cárdenas y León, and María Guadalupe Álvarez y Güitian, granddaughter of Francisco de Alarcón y Ocaña, secretary of the Spanish Viceroy and Royal Official of Veracruz (in Spanish: Secretario del Virreinato y Oficial Real de Veracruz).

[2]: 16 He enrolled at the Royal College of Mining on 26 February 1817 but suspended his studies on 1 July 1821 to join the 1st American Battalion (formerly, Regiment of the New Spain) of Agustín de Iturbide.

On 20 July 1822, he was promoted to First Lieutenant and on 23 January 1823 he began to teach Mathematics to the members of the Corps.

[2]: 29 Velázquez suffered from blindness during the last 13 months of his life, after damaging his optical nerves while doing a demonstration with one of his telescopes.

[2]: 100 The icteria velazquezi, a variety of the yellow-breasted chat classified by Charles Lucien Bonaparte in 1837, is named after him.