Rangers said: “It is with profound sadness that we announce the passing of our former manager, chairman and club legend, Walter Smith. ”
Rangers chairman Douglas Park added on the club’s website: “On behalf of the Rangers board of directors, staff and players, I convey my deep condolences to the Smith family.
“Walter leaves behind a wife, children and grandchildren, all of whom are in our thoughts and prayers at this difficult time.
“It is almost impossible to encapsulate what Walter meant to every one of us at Rangers.
“He embodied everything that a Ranger should be. His character and leadership was second to none, and will live long in the memory of everyone he worked with during his two terms as first-team manager.
“I spoke with Walter as recently as last weekend. Even when he was battling illness, he was still able to provide advice and support. For that, I am personally grateful.
“I know that he continued also to maintain dialogue with senior members of staff, including our manager, Steven Gerrard.
“Walter will be sorely missed by all of us at Rangers.
“Winning 10 top-flight titles as manager, five Scottish Cups and six League Cups, as well as leading his club to the UEFA Cup final in 2008, he will be remembered by the football community across the world.
“His spells as Scotland manager as well as managing in the English Premier League underlined his credentials as one of the great modern-day football managers.
“However, for Rangers supporters, he was much more than just a football manager. Walter was a friend to many, a leader, an ambassador, and most of all, a legend.”
The Scottish Football Association tweeted: “We are deeply saddened to learn of the passing of the former Scotland national coach, and one of the most successful managers in Scottish football history, Walter Smith.
“The thoughts of everyone at the Scottish FA are with his friends and family at this time.”
A former Dundee United and Dumbarton defender, Smith was appointed manager at Ibrox in 1991, succeeding Graeme Souness.
He won 13 major trophies in seven years, including seven league titles in succession, before leaving at the end of the 1997/98 season and subsequently joining Everton.
He stayed at Goodison Park for four seasons before a brief stint as assistant manager to Sir Alex Ferguson at Manchester United.
Smith was appointed Scotland manager in December 2004 and was in charge for three years before returning to Rangers, where he won a further eight trophies before retiring in 2011 after completing another domestic double.
Everton tweeted: “A very sad day for football. A man held in high regard by all his players. Our thoughts are with Walter’s loved ones at this tough time.”
Manchester United tweeted: “Everyone at Manchester United is deeply saddened to hear of the passing of Walter Smith.”
Scotland’s first minister Nicola Sturgeon also tweeted her condolences, calling Smith “a true football great”.