Father Murray was born in Brooklyn, New York in May 1959, and grew up in New Rochelle. He attended Regis High School and Dartmouth College. He entered St. Joseph's Seminary, Dunwoodie in 1980, and was ordained a priest on December 1, 1984. He was assigned to various parishes in the Bronx and Manhattan before being sent to the Gregorian University in Rome in 1993 to study Canon Law. He was awarded a Doctorate in Canon Law in 1998, and then served briefly as a Judge on the Metropolitan Tribunal before being named Pastor of St. Vincent De Paul Church on West 23rd Street in 1998. In 2012 Fr. Murray was named Pastor of Holy Family Church.

Fr. Murray has appeared as a commentator on religious topics on various television and radio outlets, including EWTN, EWTN Spanish, Fox News, Fox Business News, MSNBC, NY1, Radio Maria, Fox News Radio and the Voice of America. He is fluent in French, Spanish and Italian, and has a working knowledge of Portuguese. He served in US Naval Reserve Chaplain Corps from 1994 to 2005.