Green began his botanical career in 1954 as assistant botanist in the Western Australian Herbarium. He remained in that position until 1958, in his final year serving as botanical adviser to phytochemical surveys in the southwest.
He then took up a position at the University of New England at Armidale, New South Wales until 1963, when he moved to Canberra, initially as an academic, and after 1966 as a researcher at the Forest Research Institute. In 1970 he moved to Ontario, Canada, taking up a post as professor at the Laurentian University.