Gorriti was born in Jujuy to Feliciana Coeto and Ignacio de Gorriti Navarro, members of the local gentry. He and his brother, Juan Ignacio de Gorriti (later a prominent priest and lawmaker), studied at the Montserrat School in Córdoba.
Gorriti, who hailed from Jujuy, was born into a family of local nobility to Feliciana Coeto and Ignacio de Gorriti Navarro. His brother, Juan Ignacio de Gorriti, later became a renowned priest and legislator. They both received their education at the Montserrat School in Córdoba.