Burns attended Glasgow's St. Aloysius College. In 1974 he graduated in medicine from the University of Glasgow. He started a career in general surgery, and for five years he was a consultant surgeon at the Glasgow Royal Infirmary. He then changed career and became the Medical Director of the Glasgow Royal Infirmary. In 1993 he became Director of public health for the Greater Glasgow Health Board. In 1999 he was awarded a visiting professorship in public health medicine at the University of Glasgow, and he also became a senior research fellow in the School of Business and Management at the university.