Born in Norway, Michigan, he began playing the accordion at age nine and started classical study when his family moved to Chicago in 1934. In 1941 he joined Ben Bernie's band as an accordionist. He adapted Benny Goodman's music to the accordion. From 1945 to 1960 he worked for NBC, performing on The Dinah Shore Show, Tonight, The Dave Garroway Show and other radio and TV shows with Garroway. He recorded 130 episodes of the 15-minute The Art Van Damme Show for NBC Radio. He once said he did so many performances on a continual basis he never needed to practice.
Van Damme toured Europe and was popular with jazz listeners in Japan and regularly won the domestic Down Beat reader's poll for his instrument.
Van Damme was married, and had three children. After he retired to Roseville, California he continued to perform almost to the end of his life. He had been ill with pneumonia for several weeks when he died on February 15, 2010 at the age of 89.