Brennan was born in 1873 at his father's farming property at Upper Emu Creek south of Bendigo, Victoria.

Their father was active in local government, serving three terms as president of the Strathfieldsaye Shire Council.

[1] A prominent lay figure in Melbourne Catholicism, Brennan established a legal business specialising in union cases.

Although Brennan had gone into the election holding Batman with a comfortably safe majority of 25.8 percent, he was defeated by United Australia Party challenger Samuel Dennis on an unheard-of swing (the biggest in Australian electoral history until that time) of 26.6 percent.

[1] The couple had two children, with their son Niall completing biographies of Archbishop Daniel Mannix[3] and businessman John Wren.