The news comes just a week after the side’s captain, Billy McNeill, passed away at the age of 79.
Celtic confirmed that Chalmers died early on Monday morning surrounded by his family, leaving behind his wife Sadie, children Stephen, Carol, Paul, Ann, Martin and Clare, and both grandchildren and great grandchildren.
Celtic chief executive Peter Lawwell paid tribute to “legend” Chalmers, and highlighted that the short time since McNeill’s death makes the news all the more tragic.
“This is such terrible news, and on behalf of the club, I would first of all like to pass on my condolences to Stevie’s wife, Sadie, their children, Stephen, Carol, Paul, Ann, Martin, Clare, and their grandchildren,” Lawwell said in a statement.
“Stevie was a much-loved husband, father and grandfather, and our thoughts and prayers are with the family at this desperately sad time.
“This is a particularly devastating time for the Celtic Family, with the passing of Stevie Chalmers coming so soon after his friend and former team-mate, Billy McNeill. My condolences also go to the Lisbon Lions, already mourning the loss of their captain, and now grieving the death of another one of their own.
“Stevie Chalmers was a Celtic legend, and one of the greatest goalscorers this club has ever seen. Indeed, only three other legends in Jimmy McGrory, Henrik Larsson and Stevie’s close friend, Bobby Lennox, have scored more goals.”