Geoffrey Brennan did both his undergraduate and PhD degrees at the ANU in Economics. In 1968 he joined Economics at ANU as Lecturer and in 1978 took a Professorship in the Public Choice Center at Virginia Tech, Blacksburg Virginia. At Virginia Tech he began an extensive collaboration with Nobel Laureate (1986) James Buchanan, a collaboration that resulted in two monographs, The Power to Tax (1980) and The Reason of Rules (1985), and a number of articles in major journals. In 1984 he returned to the ANU to take up the Headship of Economics in the Faculties. In1988 he moved to the Research School of Social Sciences where he served as Director from 1991 to 1997. He was Head of the Social and Political Theory Program within the School from 2000 until 2003. In 2004 he joined the Philosophy Program.

Brennan's interests range broadly across rational actor political theory, economics and philosophy, and public economics. He is currently editor of the journal Economics and Philosophy, and has recently, with Hartmut Kliemt and Robert Tollison, edited the Collected Works of James Buchanan in twenty volumes. He is the author of three books in other collaborations: Democracy and Decision (1993) with Loren Lomasky, Democratic Devices and Desires (2000) with Alan Hamlin, and The Economy of Esteem (2004) with Philip Pettit. In 2001 he gave the Wittgenstein Lectures at the University of Bayreuth. In 2002, he became President of the Public Choice Society, the first non-American to be appointed in the forty year history of the Society. In 2003 he and Loren Lomasky were awarded the American Philosophical Association's Gregory Kavka Prize in Political Philosophy for their paper "Is There a Duty to Vote?".

Brennan is an enthusiastic (but scarcely competent) golfer, and a semi-professional singer (for some years a national recitalist with the ABC). He is also a practising Anglican. He is currently Vice-President of Relationships Australia (Canberra & Region) and serves on the Board of St Mark's National Theological Centre, and the ACT Branch of Musica Viva.