The first Briton to hoist the European Cup and one of the sport’s most celebrated captains, McNeill played a total of 822 games over 18 seasons, enjoyed two successful terms as Celtic’s manager and won 31 trophies during his long association with the club.
His death at the age of 79 followed a long battle with dementia.
A family statement read: “It is with great sadness that we announce the death of our father Billy McNeill. He passed away late last night surrounded by his family and loved ones.”
Dubbed ‘Cesar’ by the Celtic faithful, McNeill was the captain of the legendary Lisbon Lions side that became the first British team to win the European Cup in 1967.
He retired from playing in 1975 after winning his final trophy, the Scottish Cup, and retained a strong association with the club throughout the rest of his life, becoming an ambassador in 2009.
Six years later a statue of McNeill holding aloft the European Cup was erected outside Celtic Park.
Current Celtic manager Neil Lennon said: “When you think of Celtic and our incredible history, Billy McNeill is always one of the first names that comes to mind.”
Former Manchester United manager Sir Alex Ferguson, said Mr Mcneill was “a giant in Scottish football”.
“He was also a truly good man and will be a loss to everyone who knew him. Farewell Cesar.”