Fallon made more than 250 appearances for Celtic during the 1950s and was assistant manager to Jock Stein throughout the most successful spell in the club's history. Celtic said Fallon died peacefully on Friday morning surrounded by his family.
The club announced on their Twitter feed: "Celtic legend Sean Fallon has died peacefully at the age of 90. Our thoughts and prayers are with his family."
The Irishman unfurled the Scottish Premier League flag before the champions began the defence of their title at Celtic Park in August last year. Fallon, who made his Celtic debut in 1950, was credited with bringing the likes of Tommy Gemmell, Danny McGrain, Kenny Dalglish, Davie Hay, Lou Macari and Pat Bonner to the club.
Chief executive Peter Lawwell told the club's official website: "Sean Fallon was a Celtic legend who devoted much of his life to the club he loved. He was, of course, a supporter, first and foremost, and he was proud to have worn the green and white hoops that he loved.
"He did so with fearless distinction over eight years in the 1950s, and Sean was at the heart of all of our triumphs, including that famous 7-1 League Cup victory in 1957.
"Ten years later, he was part of our greatest ever success, winning the European Cup in Lisbon.
"Working alongside Jock Stein, Sean helped to deliver that trophy, along with nine consecutive league titles and numerous other trophies. He was an integral part of the club's success, and also played a vital role in identifying talented young players who would go on to become great Celts.
"He was a gentleman with a great sense of humour, and always a welcome guest here at Celtic Park. And there could have been no more fitting person to unveil the championship flag at this start of this, our 125th anniversary season, than a man who gave so much to Celtic Football Club.
"Sean will be sadly missed but he will never be forgotten for what he did for our club."