Smith achieved legendary status at Ibrox, with 21 trophies in two spells making him the second most successful Rangers boss ever behind Bill Struth.
He won the latter seven titles of Rangers' nine-in-a-row run in the 1990s and returned to Ibrox in 2007.
Between those stints, he had four years at Everton and two with Scotland before being enticed back to the Glasgow club.
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.
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."
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.
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.
Smith assisted Ferguson once again in 2004, joining Manchester United's coaching staff.
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