Brett was educated at the Australian National, Cambridge and Griffith Universities.
He was a Senator for Queensland from 1999 to 2015, serving in the Howard and Abbott ministries. He then served as Australia's Ambassador to the Netherlands and Permanent Representative to the Organisation for the Prohibition of Chemical Weapons.
He is now Chair of the Council of the National Library of Australia and an Adjunct Professor in the School of Justice at the Queensland University of Technology.