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.
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.
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