He has achieved international fame for appearing in Kevin Costner's Dances with Wolves (1990), which earned him an Academy Award nomination.

Other notable films include Thunderheart (1992), Maverick (1994), Die Hard with a Vengeance (1995), The Green Mile (1999), Skins (2002), Transamerica (2005), Casino Jack (2010), Winter's Tale (2014), The Shack (2017), Wind River (2017) and Shadow Wolves (2019).

[3] He worked as an audio technician for rock bands based in Newfoundland and Labrador,[4] and later related that musician Kelly Jay repeatedly encouraged him to try out for a play.

[9] On viewing his first television role, Greene stated that it was "awful", and that it prompted him to start learning to act as a profession.

As a practitioner of shamanism, his character came into direct conflict with the show's other doctor, a traditionally trained professional that (initially) had little use for unorthodox ways.

[15] In 1992, Greene played the role of Ishi, the last Yahi, in the HBO drama The Last of His Tribe,[16] and in 1994, he began appearing as Mr. Crabby Tree in the children's series The Adventures of Dudley the Dragon.

[18] He starred in the short-lived television series Wolf Lake in 2001 as Sherman Blackstone along with Lou Diamond Phillips.

He appeared as himself in a parody of the famous Lakota-brand pain reliever commercials, on CBC Television's Rick Mercer Report.

At the urging of actor Lou Diamond Phillips, Greene was cast as a recurring guest star on Longmire, which ran for six seasons from 2012 to 2017 on A&E and Netflix.

In 2024, Mr. Greene guest starred in a series, "Tulsa King" S2Ep9,Triad where he appeared as a medicine man by the name, "Old Smoke".

Greene's Academy Award–nominated role as Kicking Bird (Lakota: Ziŋtká Nagwáka) in the 1990 film Dances with Wolves showcased his talents to audiences beyond his native Canada.

"[6] He appeared in the contemporary action-mystery film, Thunderheart (1992), playing Walter Crow Horse, a gruff, savvy local cop living on an Indian reservation.

At a screening of the movie the Los Angeles Times noted that Greene, "[as a] thoroughly modern Native American who exploits his position as a tourist attraction for Russian adventurers", got the most laughs.

[24] Greene also acted alongside Bruce Willis and Samuel L. Jackson in the 1995 film Die Hard with a Vengeance, where he played Detective Joe Lambert.

[27] Greene co-starred as Slick Nakai with Adam Beach and Wes Studi in the film A Thief of Time (2004) and Coyote Waits, both adapted from Tony Hillerman novels of the same names and produced by Robert Redford.

[29] Greene provided the pre-recorded narration for Tecumseh!, the highly acclaimed outdoor show held in Ohio, based upon the life of the illustrious Shawnee chief of that name.

[30] In 2018, Greene acted as the beleaguered Native-American elder Chief Rains Fall in the western-themed video game Red Dead Redemption 2.

[citation needed] In June 2008, he was awarded an honorary doctor of law degree from the Brantford campus of Wilfrid Laurier University.