Neil Doncaster, Chief Executive of the SPFL, said:
“This is terrible news for Walter’s family and friends, and also for everyone associated with Scottish football.
“Walter was a true giant of the game with an unparalleled reputation for integrity and character.
“It was a great privilege to have met with him many times in the Blue Room at Ibrox and at grounds the length and breadth of the country during his long and illustrious career with Rangers.
“It was therefore no surprise to find, during his time on the Rangers board, that his contributions to our various discussions were hugely insightful, cogent and grounded in common sense for the betterment of the wider game.
“He will be sadly, sadly missed. but his achievements across the decades – from his time with Dundee United, Scotland, and, of course, Rangers serve as a fitting legacy for one of the true giants of our game.”
Murdoch MacLennan, Chairman of the SPFL, said:
“Walter Smith represented all that was good about our game.
“He was universally admired and respected, and with very good reason.
“His career ranks among the greatest ever in Scottish football’s long and illustrious history.
“Of course, Rangers fans hold him in the utmost regard for his long and proud association with their club, but Scottish football in its widest sense owes Walter an enormous debt of gratitude.
“He was a true football man and he will be sorely missed by his many, many friends across the game.
“Our thoughts and prayers go out to his family at this very difficult time.”