Ms MacDonald, 70, who burst on to the political scene in 1973 as a 30-year old when she won the Glasgow Govan by-election, had suffered for many years from Parkinson's disease and had campaigned for the introduction of a right-to-die Bill.
She represented the SNP at both Westminster and Holyrood, before serving as an Independent MSP. She latterly represented the Lothian region.
Her husband, former SNP deputy leader Jim Sillars, said: "My wife Margo MacDonald died peacefully at home surrounded by her family today at 1.10pm.
"She leaves a void in our lives which will be impossible to fill and her death robs the Scottish nation of one of its greatest talents.
"She was without question the most able politician of her generation. Today, the brightest light in the Scottish political firmament has gone out."
Mr Sillars said his wife's legacy would "speak for itself", adding: "She supported and inspired generations of idealists and campaigners who, like her, wanted Scotland to take its place in the world.
"Her talent acted like a magnet and she gave her time so freely to so many for so long."
While he said many would mourn her, he added: "The pain of loss will be borne most of all by those at the heart of her life - her children and her grandchildren. We will do all we can to honour her memory."
Ms MacDonald, who had two daughters, Zoe and Petra, famously won the Govan by-election for the SNP in 1973, triumphing in what had been regarded a Labour stronghold.
But she failed to hold on to the seat in the 1974 General Election.
She returned to elected politics in 1999 when she became a list MSP for the SNP in the Lothian region in the Scottish Parliament.
After being placed low down on the party's list for the area for the 2003 election, she decided to stand as an independent, and was elected in 2003, 2007 and again in 2011.
The Parkinson's sufferer campaigned for assisted suicide to be legalised, bringing two Member's Bills before Holyrood.
The first proposal was voted down by MSPs in 2010, with Ms MacDonald going on to launch a second attempt to change the law in 2013.
Her Assisted Suicide (Scotland) Bill will continue to go through Holyrood, with Green Party MSP Patrick Harvie now spearheading the proposed legislation.
While the death of a regional MSP usually results in a new member being taken from the party's list, this will not happen in Ms MacDonald's case as she was an independent. Her seat at Holyrood will instead remain vacant until the 2016 Scottish Parliament election.
First Minister Alex Salmond hailed her as "one of the great rallying figures of Scottish nationalism".
He added: From her Govan by-victory in 1973 she had a profound role in Scotland's home rule journey. Very few politicians are recognised and known to the public by their first name - Margo was. Even fewer have the profile and talent to be elected comprehensively as an independent candidate - Margo had.
"I saw her only last week to talk tactics on the independence referendum. Despite great physical infirmity, she dispensed wise advice and her enthusiasm and commitment to the independence cause was bright and undimmed."
Scottish Labour leader, Glasgow MSP Johann Lamont, said: "Margo's passing sees a bright light, and one of the biggest personalities and characters of Scottish modern political life, go out.
"Her sense of humour, passion, integrity and unflinching desire to speak truth to power, meant she came as close to a political treasure in Scotland as I think it is possible to be.
"As one half of a formidable political union with Jim, she was a trailblazer in many ways. The fact she was elected and returned as an independent by the people of Lothian, a rare feat in national politics, shows how she had become part of our political fabric.
"Her loss leaves Parliament, her much-loved Leith and her family, with a very large and painful gap that can't be filled."
Scottish Tories' leader Ruth Davidson described Ms MacDonald as being "a huge figure in Scottish politics and a complete one-off".
She added: "She sat as an independent, and independent she was - independent of thought, independent of mind and independent of spirit.
"From prostitution to assisted suicide, she was willing to champion difficult, challenging and morally complex issues to ensure they got the Parliamentary consideration they deserved."
MSP Willie Rennie, leader of the Scottish Liberal Democrats, said: "Margo was a force of nature in Scottish life. The affection for her transcends party politics and political parties.
"Her personal kindness and professional charm will be missed in the Parliament, throughout the Lothians and far wider."
Mr Harvie, a Glasgow MSP, said: "I have felt deeply privileged to work with Margo MacDonald on many issues in my time as an MSP. I have always enjoyed the wit and sparkle she brought to debates in the Chamber, but she could also offer a formidable challenge when it was needed."
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