Family friend and former agent Ray Anderson confirmed the death to ESPN's Adam Schefter after speaking with Green's wife. Anderson said Green died after a cardiac arrest.
Green's Vikings made eight playoff appearances in 10 seasons, reaching the NFC Championship Game in 1998 and 2000. He led the Vikings to a 15-1 regular season in 1998.
Robert Smith, a Fox college football analyst and former Vikings running back, posted his grief over Green's death on Twitter.
Green's Cardinals tenure might be best remembered for his "They are who they thought they were" rant after Arizona blew a 20-0 halftime lead to the Chicago Bears on Monday Night Football in 2006.
Sportswriter Larry Fitzgerald Sr., the father of Cardinals wide receiver Larry Fitzgerald, told ESPN's Josina Anderson that he spoke with Green on Thursday.
"Denny was my guy," Fitzgerald said. "He gave me the opportunity to host and produce his radio show eight years ago."
Green also served as a head coach of Northwestern and Stanford at the collegiate level.