"Dennis passed away last night from complications of cardiac arrest," Green's family said in a statement. "His family was by his side and he fought hard."
Green's Vikings made eight playoff appearances in 10 seasons from 1992 to 2001, reaching the NFC Championship Game in 1998 and 2000. He led the Vikings to a 15-1 regular season in 1998 and ranks second in franchise history in games coached, wins and winning percentage, trailing Hall of Fame coach Bud Grant in each category.
"Denny made his mark in ways far beyond being an outstanding football coach," the Vikings said in a statement. "He mentored countless players and served as a father figure for the men he coached. Denny founded the Vikings Community Tuesday Program, a critical initiative that is now implemented across the entire NFL. He took great pride in helping assistant coaches advance their careers. His tenure as one of the first African-American head coaches in both college and the NFL was also transformative."
Mike Tice, who served on Green's staff in Minnesota and succeeded him as head coach, called Green a "great motivator of men."
"Great teacher of coaches. Excellent eye for talent," Tice said. "I hadn't seen Denny in years, but I find myself quoting him: 'Plan your work and work your plan.' He taught me a lot."
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 (2004-06) 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.
"All of us at the Cardinals are incredibly saddened by the news of Dennis Green's passing. Coach Green will rightly be remembered as a true innovator, leader and pioneer among football coaches," Cardinals president Michael Bidwill said in a statement. "We express our deepest sympathy to his family and his many friends."
Quarterback Kurt Warner, who joined the Cardinals in 2005, tweeted his thoughts on Green's death.
Green had a career record of 113-94, and he went 4-8 in the playoffs. He was the second black head coach in the NFL's modern era; the Vikings hired Green three years after Art Shell became the Raiders' head coach.
"We are saddened to hear the news of Dennis Green's passing," Troy Vincent, the NFL executive vice president of football operations, said in a statement. "Denny was a terrific head coach and inspired his players on and off the field. He helped pave the way for minority coaches and recently served as a key advisor on the NFL's Career Development Advisory Panel. On behalf of the NFL, our thoughts and prayers go out to the entire Green family."
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."
He served as an assistant to Bill Walsh on the dominant San Francisco 49ers teams of the 1980s.
Green enrolled at Iowa and played running back for the Hawkeyes from 1968 to 1970. He played for the BC Lions in Canada in 1971 before returning to coach in college, beginning at Dayton in 1973 and gradually climbing to bigger programs.
ESPN's Adam Schefter and Vaughn McClure, ESPN Stats & Information and The Associated Press contributed to this report.