Sir Andrew Smith was educated at Wyggeston Grammar School in Leicester and at Wadham College Oxford, where he took degrees in classics and then in law. He was called to the Bar by Middle Temple in 1974, and became a member of Fountain Court Chambers. Although commercial law was the main focus of his practice, he was also involved in Chancery litigation and some cases at the Parliamentary Bar. He was appointed Queen's Counsel in 1990, and was a Recorder from 1996 to 2000. He also sat as an arbitrator. He became a Queen's Bench Judge in 2000, and was nominated to sit in the Commercial Court, where he was Judge In Charge from 2008 to 2009. While on the Bench, he also sat in the Chancery Division, and he was a Presiding Judge on the North Eastern Circuit from 2003 to 2006.

After retiring from the Bench in 2016, Sir Andrew became a Judge of the Abu Dhabi Global Market Courts and returned to sitting as an arbitrator.