Young joined the Hoops in 1961 and spent seven years with the club during an era in which Jock Stein's leadership transformed Celtic from the also-rans of Scotland into European champions.
He may very well have been part of the Lisbon Lions side which became the first British side to conquer the continent had it not been for an injury which allowed the likes of Willie O'Neill and then Jim Craig to steal in front for the right-back slot.
In a statement, the Scottish champions said: "Everyone at Celtic Park was saddened to hear that former Celt, Ian Young who played for the club from 1961 until 1968, passed away suddenly after illness at the age of 76.
"The thoughts and prayers of everyone at Celtic Football Club are with the family and friends of Ian Young at this sad time."
Young joined Celtic from Neilston Waverley and scored three goals in 133 Celtic games before returning to Renfrewshire in 1968 to join St Mirren.
He had made his Buddies switch in a bid for more first-team action but sadly suffered a cruciate ligament knee injury soon after and saw his professional career cut short at just 27.
But he will still be remembered fondly at Celtic Park.
He was a regular in the side when Stein arrived and starred as the club ended an eight-year trophy drought with their 1965 Scottish Cup triumph and he was also in the team which overcame Rangers in the League Cup final later that year.