Garibi was educated at the Colegio del Señor San José (primary education) and the Seminary of Guadalajara from 1900 to 1906, where he studied the humanities, sciences, Latin, Greek, philosophy and theology.

He was named professor of Latin at the Seminary of Guadalajara in 1911, and occupied the post until 26 August 1913.

He then went to Rome to study at the Pontifical Gregorian University from October 1913 to July 1916, where he earned a doctorate of theology and a licentiate in canon law.

In 1929 the Archbishop of Guadalajara, José Francisco Orozco y Jiménez, was expelled from the country during the course of the government's attempt to suppress the Catholic Church.

Garibi was made a Cardinal Priest, with the titular church of San Onofrio in the consistory of 15 December 1958 by Pope John XXIII.