Archbishop Brown graduated from the University of Notre Dame in 1981 with a major in history. He then studied theology at Oxford University and medieval studies at the Pontifical Institute of Mediaeval Studies at the University of Toronto. In 1989, he was ordained a priest for the Archdiocese of New York. He did parish work at St Brendan's Parish in the Bronx, New York City, before being sent to Rome for doctoral studies in sacramental theology at the Pontifical Atheneum of Saint Anselm. He worked at the Congregation for the Doctrine of the Faith from 1994 until 2011 when he was appointed Apostolic Nuncio to Ireland.