Brodie grew up in Alloa, Clackmannanshire and was educated at Dollar Academy in Clackmannanshire, and studied the School of Law of the University of Edinburgh (LL.B.) and the School of Law of the University of Virginia in the United States (LL.M.). He was admitted to the Faculty of Advocates in 1976, taking silk in 1987. He is the son of the late Very Rev Dr Peter Brodie, former minister at St Mungo's Parish Church, Alloa, and Moderator of the General Assembly of the Church of Scotland in 1978-79.
In 1983, Lord Brodie married Carol Dora McLeish, with whom he has two sons and a daughter. His recreations include fencing, walking and reading, as well as being the Chairman of the Council of the Cockburn Association.