Greene's first brushes with the entertainment industry came when he was an audio technician for rock bands. He graduated from The Centre for Indigenous Theatre's Native Theatre School program in 1974, and began appearing in theater in Toronto and England.
His screen debut was in 1983 in Running Brave, and appeared in such films as Revolution and Powwow Highway, but it was his Academy Award nominated role in the 1990 film Dances With Wolves that brought him stardom.
In 1997, Greene suffered a major depressive attack, and had to be hospitalized after a police encounter. He survived the ordeal, making such movies as The Green Mile. He starred in the short-run television series Wolf Lake in 2001.