Neighbour, who played in Spurs' 1971 League Cup-winning side, suffered a heart attack at home while recovering from a hip replacement operation.
Neighbour was on Tottenham's books from 1966 to 1976 and returned to the club in 2000 as coach of the under-17 side.
He also represented Seattle Sounders and played the last of his 304 Football League games on loan at Bournemouth.
He made his debut for Spurs against Stoke in October 1970 and playing his final game for the Cherries against Wrexham in 1983.
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Pay your tributes to Jimmy Neighbour
Before rejoining Tottenham he spent four years as a coach at Enfield, helping them win the FA Trophy in 1988.
He was also youth development officer at West Ham, assistant manager at Doncaster and boss at St Albans.