The former Scotland manager's family confirmed the news on Monday.
"Craig died peacefully today after a short illness in University Hospital, Ayr, surrounded by close family members," read a statement.
"The family wish to express their deep appreciation of the outstanding care and attention provided by hospital staff and the countless messages of support and sympathy from friends and colleagues. At this particularly sad time the family now requests that their privacy is respected during the grieving process."
Brown's former club Aberdeen also paid tribute to Brown in an emotional statement.
"Everyone at Aberdeen FC is heartbroken by the loss of our beloved former manager, director and club ambassador, Craig Brown," read a club statement.
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"A dear friend to us all, Craig will be sorely missed and our love and condolences are with his family at this terribly sad time."
Scotland appointed Brown as manager in 1993 and saw the former Rangers boss guide the national team to Euro 96 and World Cup 98 in France.
Brown's eight years in charge of the Tartan Army means he remains Scotland's longest-serving manager, after taking in 71 games at the helm of the national team.
A playing career that featured spells at Rangers, Dundee and Falkirk was cut short by a knee injury and led Brown into management.
Brown started off with Clyde before joining up with Scotland to work as part of Alex Ferguson's backroom staff and then as Andy Roxburgh's assistant.
Roxburgh was replaced by Brown in 1993 and remained in his post until resigning in 2001 after failing to qualify for World Cup 2022.
Brown went on to manage Preston, Motherwell and Aberdeen before retiring from management in 2013. He was awarded a CBE in 1999 for services to football.