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.
Former Vikings running back Robert Smith, now a FOX Sports college football analyst, posted a message on Twitter.
"Rest in peace Denny. I lost my mother in April, I feel like I just lost father," Smith tweeted
Green made eight playoff appearances in 10 seasons with the Vikings and reached the NFC Championship Game in 1998 and 2000. He led the Vikings to a 15-1 regular season in 1998.
Green finished his career in 2006 with a 113-94 overall record in 13 seasons as a head coach and a 4-8 mark in the postseason.
Green spent 17 years as a coach in the NFL. He was a special teams coordinator with the San Francisco 49ers for a season and later their wide receivers coach for three seasons in the 1980s.
After a stint as the head coach of Stanford University, Green returned to the NFL and led the Vikings from 1992 through 2001. He returned three years later as the head coach of the Cardinals from 2004 through 2006.
Green also served as a head coach at Northwestern.