Green considered becoming a cartoonist after leaving High School. He studied architecture at the Melbourne Technical College because his mother warned he'd starve as a cartoonist.

Aged 18 he enlisted in the Army and served in New Guinea during the second world war. He drew cartoons for the army's newspaper.

After the war, he resumed architectural studies, but transferred to an art course at the National Gallery of Victoria.

During this time, he submitted cartoons to the Melbourne Herald. While the paper's political cartoonist, Sammy Wells, was on leave for six weeks in 1946, Green filled in. He became a staff artist in 1947 and continued as a political cartoonist for the paper until he retired in 1986. In 1949, he introducing the daily cartoon 'WEG's Day', a single-column topical comment, humorously presented, that ran for 38 years.

Green contributed cartoons to Man magazine, The Bulletin and the New York Times.

Green worked as a caricaturist and illustrator, with art in cricket books by Max Walker, on stamps and in children's books. In the 1954 VFL season, Green began a continuing tradition of posters of the winning teams.