He studied at the Seminary in Ourense and took the holy orders in 1922. Then he studied at the Pontifical University in Santiago, taking his degree in Theology. He was the parish priest in several towns and worked as teacher at the Seminary in Ourense and Valladolid.In 1945, he became bishop of Mondoñedo, where he did an important work. However, he occupied this post for a short period because in 1949 he was nominated archbishop in Santiago and cardinal in 1952.He was one of the great promoters of the construction and restoration of the archdiocese. In 1957, the Small Seminary was formally opened, the restoration works of the Big Seminary and archaeological excavations went on in the cathedral, where Bishop Teodomiro's tomb was found.Another great innovation was the introduction of liturgy in Galician language, being the first cardinal who celebrated the Mass in Galician language. The Galician Academy nominated him as academician of honour for defending Galicia. Cardinal Quiroga founded the Institute of Studies about St James as well as the magazine Compostellanum.
In addition to other values in his ecclesiastic career, he was nominated as member of the preparatory commission of the Second Vatican Council and the first president of the Spanish Episcopal Conference.Cardinal Quiroga also promoted pilgrims towards St James's tomb during his regency in the diocese of Compostela and fought in favour of the poor, promoting the construction of council houses and all sort of help.