Smith took charge at Goodison Park boss in June 1998, succeeding Toffees legend Howard Kendall.
He spent almost four seasons as manager during a precarious financial period, with several key players such as Duncan Ferguson, Marco Materazzi, Olivier Dacourt and Nick Barmby sold to raise funds.
His greatest win as Everton boss came in September 1999 when he masterminded a 1-0 defeat of Liverpool in the Merseyside derby at Anfield.
Smith was relieved of his duties in March 2002 when replaced by David Moyes.
During his managerial career, he had two spells with Rangers between 1991-1998 and 2007-2011. In total, he guided the Ibrox side to 10 Scottish Premiership titles, five Scottish Cups, six Scottish League Cups and the Uefa Cup final.
He also had a spell as Scotland manager between 2004-2007 and was assistant manager to Sir Alex Ferguson at Manchester United for a period.
Rangers chairman Douglas Park said: “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.”
Everton paid tribute to Smith and sent out their thoughts to his family during the sad time.
Former Everton striker Kevin Campbell, who was signed on loan in March 1999 and scored nine goals in eight games to keep the Blues in the Premier League before joining permanently, thanked Smith for bringing him to Goodison.
The Scottish FA sent out their deepest symapthy for one of the country’s greatest ever manager.
Ex-Celtic striker Chris Sutton called Smith a true gentleman.
Liverpool defender Andy Robertson believes Smith’s legacy will continue to live on in football despite his passing.