The former first minister had made a speech at the Institute for Cultural Diplomacy Forum before collapsing at lunch in a crowded room.
In a statement released by the Alba party, Mr Salmond’s family said he was “a devoted and loving husband, a fiercely loyal brother, a proud and thoughtful uncle and a faithful and trusted friend”.
Mr Salmond’s family said: “Alex was a formidable politician, an amazing orator, an outstanding intellect and admired throughout the world.
“He dedicated his adult life to the cause he believed in – independence for Scotland.”
They added: “In our darkest of family moments, he was always the one who got us through, making this time even more difficult, as he is not here for us to turn to. His resilience and optimism knew no bounds.
“He led us to believe in better. Without Alex, life will never be the same again.
“But he would want us to continue with his life’s work for independence, and for justice, and that is what we shall do.”
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Scottish First Minster John Swinney said Mr Salmond “left a fundamental footprint on Scottish politics” as he paid tribute to his late former party leader.
The Alba Party said it understood Mr Salmond had suffered a heart attack, although there will be a post-mortem examination to confirm the cause of death.
Speaking on Sunday With Laura Kuenssberg, Mr Swinney said Mr Salmond had also “inspired a generation” to believe in independence.
Mark Donfried, director of the Academy for Cultural Diplomacy, told the PA news agency said he witnessed Mr Salmond’s collapse at the conference in North Macedonia.
“He was here the last few days, he gave excellent participation two days ago at the panel discussion,” he said.
“He was really in the best of spirits, the best of health, and I was sitting across from him at lunch yesterday when all of a sudden he just went out and fell into the arms of a colleague of mine on the other side of the table.
“I immediately got up and ran to call an ambulance and when I came back, he was on the floor.”
Mr Salmond served as first minister of Scotland from 2007 to 2014 and was leader of the SNP on two occasions, from 1990 to 2000 and from 2004 to 2014.
He resigned as first minister after the 2014 Scottish independence referendum resulted in a 55% to 45% vote to stay in the UK.
He launched his rival Scottish independence party, Alba, in 2021 after his relationship with his successor Nicola Sturgeon fractured.
His final post on X, formerly Twitter, shortly before his death, ended “Scotland is a country not a county”.
Tributes from political contemporaries praised him for his decades in politics and efforts to move Scotland closer to independence.
His former colleague Nicola Sturgeon acknowledged the “breakdown” of her relationship with Mr Salmond but praised him for taking Scotland to the “brink of independence”.
“He was my mentor, and for more than a decade we formed one of the most successful partnerships in UK politics,” she wrote.
A commemoration for Mr Salmond was also held in the North Macedonian city of Ohrid, attended by President Gordana Siljanovska-Davkova, who is reported to have extended her condolences over the death of the former first minister.
A Foreign Office spokesperson said: “We are supporting the family of Alex Salmond, former first minister of Scotland, who died in North Macedonia on Saturday. The FCDO is in touch with the local authorities.”
