Bill, who played for the club between 1944 and 1945, was the oldest living Celtic player.
As revealed in later editions for yesterday's Evening Times, he passed away peacefully at his home in Muirkirk, Ayrshire on Monday.
Born on November 30, 1919, Bill joined Celtic from Hibernian in September 1944 following two public trial games when he played alongside Bobby Evans. He made his debut for the club in February the following year in a League Cup qualifying section game against Clyde that finished 0-0.
An inside-right, he was a miner throughout his working life and did a double-shift on a Monday so that he could play football on the Saturday.
In a statement, Celtic said: "The thoughts and prayers of everyone at Celtic are with Bill Boland's family and friends at this sad time."
Bill scored two goals for the club. The first of those came in a 3-2 win at Celtic Park against Falkirk and he scored the only goal of the game in the next tie against Partick Thistle.
Speaking to Celtic View in 2009, Bill said: "It was great to be a Celtic player, just to play with some of the players I played with and represent the club was a great honour.
"I only played four games but the fact I played those four games, I am very proud of that."
Bill, who was a guest of the club in February 2009 at the age of 89, took a bow on the Celtic Park pitch at half-time in a match against Hibernian.