Gibson was born at Little Balsier in the parish of Sorbie, Wigtownshire, on the 17th of May, 1873, son of the local schoolmaster. Later, Gibson became a solicitor in Glasgow, and joined the Glasgow CC in 1901.
Apart from his successes in Scottish chess, Gibson also played in several other tournaments and British Championships, and was always a dangerous opponent. In 1912 he was 4th and in 1913 he was 5th. He also played in the 1914 tournament, and in the 1923 British Championship he defeated Yates in the last round, depriving Yates of the title.
One of his very best performances was at the Ramsgate Easter Congress of 1929. In Premier “A” he scored 5½, winning first prize against such redoubtable experts as J.A.J Drewitt 5, L. Rellstab 5, A. Gibaud 3, D. Noteboom 3, A.G. Conde 2½, J.H. Morrison 2½, and H.H. Cole 1½. He scored 5½ points from the first six rounds, his only loss being to Drewitt in the last round, when he had already secured first place.
Not only was he an outstanding player of his time, he was also an organiser and administrator, having held at one time or another almost every post in the Glasgow CC and the Scottish Chess Association, as well as being a member of the Council of the British Chess Federation.
Note: William Gibson was married in 1916 to Miss Margaret Buick. His wife was the successful owner of 'Miss Buick's' tea room at 147 West George Street, Glasgow. She would later open another tea room at 19a Renfield Street, Glasgow. She continued to operate the business as 'Miss Buick's', and her tea rooms were used by Glasgow chess players and clubs over the years.