Born in Ireland, the son of Martin (a farmer) and Sarah (née Tobin) Brennan, Martin Brennan migrtaed to Australia in 1859, aged 20, and joined the New South Wales mounted police under the command of a Captain Zouch. Initially stationed at Braidwood he ran the gold escort to Goulburn for two years and was involved in the Lambing Flat riots at Young. Brennan was wounded in the arm during the riots and had four horses shot from under him.
By 1862 he was a senior constable at Moruya, on the New South Wales south coast. He married Elizabeth McKeon, from Galway, on 4 July 1865 and his only child, Sarah Octavia, was born on 14 April 1867. Brennan served the police force with some distinction and rose through the ranks to superintendent. His postings included Araluen, Queanbeyan (1872), Young (1880), Wagga Wagga, Newcastle (1886) and Tamworth (1894), before being recalled to Sydney to take charge of the training depot and the eastern districts. By 1902 he was superintendent of the Mounted Police Barracks at Moore Park. Brennan was one of the first policemen to achieve success with Aboriginal trackers. Among his other achievements were his handling of the coalminers' strike at Newcastle in 1888 and the high standards he achieved in the training of recruits.
Brennan took a particular interest in his daughter's education. He studied Latin and French by correspondence and he and Sarah both matriculated and gained entry to the University of Sydney in 1885. Brennan was unable to sit for a degree because he could not attend lectures, but he followed Sarah's courses in classical philology and history, which she pursued through to Masters level (1891), as well as later studying science and obtaining a B.Sc. in 1898. This learning is evident in his writing, for example, Reminiscences of the Gold Fields, a project encouraged by his daughter,contains frequent classical and literary allusions.
Reminiscences was published in 1907, the year that Brennan retired, on 1 February. He died in 1912 of a strangulated femoral hernia, his wife having predeceased him. Brennan is buried in the Catholic section of the Waverley cemetery. He was also the uncle of journalist/editor/publisher Martin C. Brennan.