Swan, born in 1930 in Connecticut, USA to Scottish parents, relocated with his family to Carnoustie, Scotland at a very young age. After completing his National Service, Swan pursued his education at various institutions, including the Dundee College of Art, Patrick Allan Fraser's Hospitalfield House in Arbroath, and the Trinity College of Music in London. His artistic journey began with exhibitions at the Scottish Royal Academy, where he was awarded a scholarship in 1954 to study in London.

In 1958, Swan received a prestigious British Council Scholarship that took him to Italy, exposing him to the vibrant contemporary art scene in Milan. During the late 1960s, Swan and his wife moved to Switzerland, where he established himself as a significant figure in abstract painting. Despite his travels, Swan frequently returned to Carnoustie, drawing inspiration from the place where he grew up and creating artwork there.

In recognition of his talent, Swan was honored with the Art Prize of the city of Bonn in 1986. Throughout his career, he showcased his artwork in both solo and group exhibitions across the United Kingdom, Italy, Germany, and Switzerland. His works have found homes in public and private collections in countries such as the UK, Brazil, Germany, Switzerland, and the Netherlands.