William Burns trained at Glasgow School of Art and at Hospitalfield Art College, Arbroath. He was elected an Associate of the Academy in 1956 and a full Academician in 1970. He was a native of Glasgow, but went to Aberdeen in 1954 as a Lecturer in Art Education at Aberdeen College of Education and later became Principal Lecturer and Head of the Art Department there. He relinquished this post in September 1970, to devote himself full time to his painting.

His professional outlook was contemporary and he was an artist who possessed a very fine colour sense. He executed all his work with great conviction and a powerful sincerity. The lyricism of his earlier landscapes and mountain scenes of the north later gave way to the more pronounced and abstracted works of the north-east, particularly harbour scenes, and within the last year his avenue of research had begun to encompass northern mining areas.

William Burns had several one-man shows, including one at the Edinburgh Festival in 1968, and his works are on show at many Local Authority Galleries in Scotland. He was a member of the Aberdeen Art Gallery Purchasing Committee.