Brennan was ordained a priest for the Archdiocese of Washington May 15, 1976. He obtained a bachelor's degree at Brown University and attended Christ the King Seminary in New York and the Pontifical Gregorian University in Rome where he received a bachelor's and master's in theology.
He spent a year in the Dominican Republic doing "Hispanic Immersion Studies" in the 1980s, and served as a pastor at several parishes, providing pastoral ministry to the Hispanic community at St. Bartholomew parish from 1988-1989.
The bishop previously held the position of director of priestly vocations and priestly programs for the Archdiocese of Washington and has been a member of the Priests' Council and the College of Consultors. He was Vicar Forane of "Northwest Deanery West" from 2002-2005 and Advocate of the Metropolitan Tribunal of the Archdiocese of Washington in 2006.
In 2005 Brennan was given the title of Monsignor. In addition to English, he speaks Spanish and knows French and Italian.
Brennan said that he wants to prioritize poverty alleviation in the West Virginia diocese.
"A primary focus will be on the poverty that those in the rural areas of the state face. I will depend on those who are working to alleviate their suffering and to determine how we can increase the Church's outreach and impact – particularly for those who have fallen victim to opioid addiction," Brennan said.
"Although there is great need across the state, there are also tremendous assets. It will be my priority to harness the resources of the diocese to serve the considerable needs while also bringing about a new era of renewal of our faith," he said.