Born to Scottish parents in Connecticut, USA, in 1930, Swan and his family moved to Carnoustie, on the east coast of Scotland when Swan was only four months old. After completeing his National Service, Swan studied at the Dundee College of Art, Patrick Allan Fraser's Hospitalfield House, Arbroath, and Trinity College of Music, London. Swan began exhibiting at the Scottish Royal Academy, and, in 1954, was awarded their scholarship to study in London.
In 1958, Swan was awarded a British Council Scholarship to study in Italy, where he enjoyed the vibrant contemporary art scene of Milan. In the late 1960's, Swan and his wife moved to Switzerland, where he established himself as an important abstract painter. Throughout his life, Swan would often return to Carnoustie, where he continued to produce work and draw inspiration.
In 1986, he was awarded the Art Prize of the city of Bonn. During his career, Swan showed in solo and group exhibitions throughout the UK, Italy, Germany and Switzerland. His works are held in public and private collections in the UK, Brazil, Germany, Switzerland and the Netherlands.