He was just sixteen when he made his VFL debut in 1974 for St Kilda. In 1980 he joined Hawthorn and was a key player during a successful decade for the club. He won the VFL Players Association Most Valuable Player award, now known as the Leigh Matthews Trophy, as well as Hawthorn's best and fairest honours in 1984. The following year he earned All-Australian selection. Greene's last game was their 1988 grand final win over Melbourne, his third premiership.
Since retiring from football, Greene has worked as a PE teacher, first at Melbourne Grammar, and currently (2011 – present) at Marnebek School in Cranbourne.