William Newbigging was born in Lanark, the son of a Writer to the Signet. He served an apprenticeship to Forrest Dewar, a surgeon apothecary in Edinburgh.
For many years, he was a surgeon in the Royal Infirmary and he was considered a dexterous operator with a reputation as a lithotomist. He also achieved some fame for a successful case of ligature of the external iliac artery which had only been done once before. His most famous junior was James Syme who was his Clinical Clerk for a time.
Despite his operative skill, he was, in those preanaesthetic days, primarily a general practitioner and, according to Sir Robert Christison, Professor of Medical Jurisprudence, he was one of the best in Edinburgh.
Christison was however upset at his acceptance of a knighthood which, he said ‘was the reward of the political services of a relative’ rather than for any contribution to medicine or surgery. He was knighted at St James Palace in 1838 by Queen Victoria on the occasion of her Coronation.
In 1828 he was appointed, with Christison, to conduct a post-mortem examination on Margery Campbell, the last of Burke and Hare's victims.
He was President from 1814 to 1816 and served on the Hall Committee for the Playfair Building.
Two of his sons, Patrick and George, became Fellows and Patrick was President from 1861 to 1863.