Motherwell-born Gemmell, who played as a left back for Celtic between 1961 and 1971, made more than 400 appearances for the Hoops, scoring 64 goals in the process.
He scored the equalising goal against Inter Milan in the 1967 European Cup final, ignoring team orders for one full back to remain in defence at all times.
One of just two Britons to score in two European Cup finals - the other being Liverpool’s Phil Neal - Gemmell scored in the 1970 final against Feyenoord, which Celtic lost after extra tine.
He later moved onto Nottingham Forest, Miami Toros and latterly Dundee, whom he later managed and led to victory in the Scottish League Cup final over former club Celtic.
Gemmell also had two spells as manager of Albion Rovers.
A Scotland international between 1966 and 1971, Gemmell also played in the famous 3-2 victory over England at Wembley in 1967.
A statement on celticfc.net read: “Tommy Gemmell is a true Celtic legend, part of the greatest side in the club’s history and a man who played a pivotal role in our greatest ever triumph when, in Lisbon’s Estadio Nacional, 11 men all born within a 30-mile radius of Celtic Park, beat Inter Milan to win the European Cup.
“And, like the rest of the Lions, Tommy remained humble about his incredible football achievements.
“The whole Celtic Family is mourning his passing, and everyone associated with the club sends their thoughts and prayers to his family, his fellow Lions and his many friends at this desperately sad time.
Our thoughts are with Mary and Tommy’s family and friends at this very difficult time.”