Former Newcastle boss Kinnear dies aged 77
Republic of Ireland defender Kinnear, who starred for Tottenham in the 1960s and '70s, was diagnosed with dementia in 2015.
He won several trophies with Tottenham before becoming a well-regarded manager for a host of Premier League teams.
"We are sad to announce that Joe passed away peacefully this afternoon surrounded by his family," a statement said.
AFC Wimbledon hailed Kinnear as a "true legend of the club" after a seven-year spell with the Dons that included an LMA Manager of the Year award in 1994 and three top-10 finishes with the 'Crazy Gang'.
The League Two club wrote on X: "Everyone connected with Wimbledon was deeply saddened to hear the news that our former manager, Joe Kinnear, has passed away.
"A true legend of the club, Joe gave us some amazing memories that we treasure.
"Our deepest condolences go to his family at this difficult time."
Kinnear joined Tottenham as a teenager in 1963 before making his debut in 1966.
He spent the next decade at White Hart Lane, lifting the FA Cup in 1967, the UEFA Cup in 1972 and the League Cup in both 1971 and 1973, making more than 250 appearances for the club.
Kinnear began his coaching career in Asia, working in the United Arab Emirates and Malaysia, before spells with India and Nepal.
He returned to England to become Dave Mackay's assistant at Doncaster and was named Wimbledon boss in 1992.
Kinnear guided Wimbledon to the semi-finals of both the FA Cup and League Cup in 1997.
However, he suffered a heart attack before a league game against Sheffield Wednesday in 1999 and stood down later that year.
He returned as director of football at Oxford before taking on a similar role at Luton, where he would appoint himself as manager and guide the club to promotion from the Third Division during the 2001-02 season.
He took the Forest job in 2004 and later replaced Kevin Keegan at Newcastle in 2008.
In 2009, Kinnear was taken to hospital after feeling ill ahead of a match against West Brom.
It was later announced he needed a heart bypass operation, effectively ending his last managerial role.