Born in Santiago de Guatemala, present day Antigua Guatemala, towards the end of the 17th century, Quirós had a religious education while pursuing his musical apprenticeship and reaching the level of a journeyman. Having taken Franciscan orders, he was put in charge of the Franciscan press, where he served until 1738, when he was appointed chapel master of the cathedral choir and orchestra. He served in this capacity for 27 years, until his death in 1765. As chapel master, he was in charge of the education of choir boys and apprentices, besides conducting the cathedral liturgical music. Among his pupils, the most outstanding was Rafael Antonio Castellanos.
Quirós is the first musician in the New World to receive a critical review. On the occasion of the ceremonies that elevated the Bishopric of Guatemala to the rank of an Archbishopric, Quirós provided liturgical music during the nine days of celebration in November, 1745. Writer Antonio de Paz y Salgado, a high official in the Spanish colonial government, published his enthusiastic review of these musical performances two years later in Mexico City.
A considerable number of Quirós' works are contained in the archive at GuatemalaCathedral.
Besides arranging a sizable amount of music sent from Spain, Lima, and Mexico City, Quirós also provided a number of original villancicos, sacred songs, and cantatas for matins of different feasts of the Catholic year:
