Born in 1934 in Portland, Maine, Brennan attended Boston College and the University of Maine School of Law, and became Cumberland County District Attorney before winning election to the Maine House of Representatives (1965-1971) and State Senate (1973-1975). His first statewide candidacy was for Governor in 1974; he lost the Democratic nomination to George J. Mitchell, whom he would later appoint to the U.S. Senate. Appointed State Attorney General in 1975, Brennan ran for Governor again in 1978, winning the primary and general elections. Brennan was reelected in 1982, serving as Governor from 1979 to 1987. In 1986 he ran for the U.S. House in Maine's First Congressional District and won with 53f the vote.

After two terms in the House, Brennan ran for Governor again in 1990, losing to Republican John McKernan. He ran again in 1994, losing to Independent Angus King but placing second, ahead of Republican Susan Collins. He would face Collins in another statewide election in 1996, running for the U.S. Senate seat being vacated by Bill Cohen, which Collins won.

In 1999, President Clinton nominated Brennan to serve as a commissioner on the Federal Maritime Commission, a small independent agency that regulates shipping between the U.S. and foreign countries. He was renominated (by President Bush) and confirmed for a second term at the FMC in 2004.