Gemmell scored Celtic's equaliser and played a part in Stevie Chalmers's 84th-minute winner as Celtic came from behind to beat Inter Milan 2-1 in Lisbon in the 1967 final.
It made them Britain's first European champions and saw the team dubbed 'the Lisbon Lions'.
"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," Celtic said in a statement.
Gemmell also scored in the 1970 final, when Celtic lost 2-1 to Dutch side Feyenoord in Milan.