Born in Bloomington, McLean County, Illinois, Brennan attended parochial schools.

He was admitted to the bar the same year and commenced practice in Bloomington, Illinois.

Brennan was elected as a Democrat to the Seventy-third and Seventy-fourth Congresses (March 4, 1933 – January 3, 1937).

He resumed the practice of law in Bloomington, Illinois, until his death there on July 4, 1941.

This article incorporates public domain material from the Biographical Directory of the United States Congress