Andrew Wood was born in Edinburgh and educated at the High School and Edinburgh University. After graduation, he was appointed Medical Officer of the New Town Dispensary. On his father's death, he succeeded him in several important public appointments. He was surgeon to Heriot's Hospital and to the Merchant Maiden and Trades Maiden Hospitals. He was Inspector of Anatomy for many years and, for a time, was a manager of Edinburgh Royal Infirmary.
He represented the College on the General Medical Council from its institution in 1858 until he was succeeded in this office by Sir John Struthers.