His second spell in charge delivered three more titles and a Uefa Cup final appearance, in 2008.
His death comes in the same year Rangers clinched their first top-flight title since Smith’s final season in charge in 2011.
Posted with a picture of him and Smith on Instagram, Rangers manager Steven Gerrard said: “Thank you for all your wisdom, support and friendship. You meant the world to everyone at Rangers.”
In a club statement announcing the news, chairman Douglas Park added: “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. 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.”
Ally McCoist, who played in Smith’s 1990s Ibrox team and was later his assistant manager with Scotland and Rangers, told Talksport: “He was my boss, my coach, my second father and then turned into one of my best friends.
“The loss is absolutely incredible. He was the best husband, father, friend, everything you want from a man. I can’t tell you how devastated I am.”
Former Everton defender Alan Stubbs also paid tribute, telling BBC Radio 5 live: “Walter gave me the opportunity to fulfil my dream to sign for Everton and become captain.”
Player, assistant, manager & chairman
As a defender, Smith played more than 200 games for Dundee United, where he began his coaching career under Jim McLean at the age of 29 when a pelvic injury forced him to retire early.
He also turned out for Dumbarton and was assistant to Sir Alex Ferguson at the 1986 World Cup, but it was as a manager where Smith made his mark.
After moving from Tannadice to Rangers in 1986 as Graeme Souness’ number two, he took sole charge in 1991 and embarked on a near-decade of dominance – including the domestic treble in 1993 – to equal Celtic’s record of nine successive titles in 1997. He was awarded an OBE for services to football the same year.
Smith assisted Ferguson once again in 2004, joining Manchester United’s coaching staff.
Following the end of his second stint as Rangers manager, Smith had a three-month spell as Ibrox chairman in 2013 but resigned the position after a period of bitter infighting within the boardroom.
Rangers confirmed in March that Smith was recovering in hospital following an operation.
And his passing comes 10 months after McLean, whom he assisted over a long spell at Dundee United, died at 83.
“Walter leaves behind a wife, children and grandchildren, all of whom are in our thoughts and prayers at this difficult time,” added Park.
Rangers, who host Aberdeen on Wednesday, asked for the Smith family’s privacy to be respected.
And Everton said in a statement: “Everton Football Club is deeply saddened to learn of the passing of the club’s former manager, Walter Smith OBE.
“The Scot was a tremendously popular figure at Everton, players and staff unanimously warming to Smith’s genial and empathetic nature.”