Fr. Brady was born in Philadelphia, PA to Dr. Eugene F. and Joan J. Brady. He is one of seven children, and his older brother is a priest serving the Archdiocese of Philadelphia. His father was a permanent deacon for the Diocese of Baton Rouge.  After high school, Fr. Brady attended Spring Hill College in Mobile, AL and received a BS in Accounting in 1987. He then attended the University of Mississippi School of Law and received a juris doctorate in 1990. He then moved to Lafayette where he practiced law for 11 years.

In 2001 Fr. Brady entered formation for the priesthood and attended Notre Dame Seminary in New Orleans. He was ordained a deacon in January of 2006 and a priest in July of the same year. After ordination, he was assigned to study Canon Law at Catholic University of America in Washington, D.C. and received a licentiate in canon law in May of 2009. Upon his return from Washington, Fr. Brady served as associate pastor of St. Michael’s Church in Crowley until 2010, pastor of St. Landry Catholic Church in Opelousas from 2010 until 2018, and was named pastor of St. Pius X Church in Lafayette in July of 2018.