His eulogy, delivered at Inverness Cathedral on Saturday afternoon, paid tribute to the 93-year-old former MP, MEP and MSP, affectionately known as Madame Ecosse.
Ms Ewing, the party’s first female MP, died surrounded by relatives last month.
Her children Fergus, Annabelle – current SNP MPs – and Terry watched as the service paid tribute to the “beloved icon”‘s decades of political service.
In his eulogy, Mr Salmond recalled Ms Ewing’s “instinctive and heartfelt” commitment to Scotland.
Ms Ewing was best known for declaring after her surprise victory in the Hamilton by-election in 1967: “Stop the world, Scotland wants to move on.”
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Mr Salmond said: “Could any other politician have won Hamilton? Possibly. Would they have done it too and used it as a launch pad to change Scottish politics forever and ever? No chance. That was Winnie Ewing’s accomplishment.”
He said the SNP icon tipped the axis of Scottish politics and “put Scottish independence on the map”.
And he said Ms Ewing should be remembered as “the true radical spirit of Scotland”, a phrase once used to describe Scottish bard Robert Burns.
The service was conducted by the Rev. Mark Strange, Primus of the Scottish Episcopal Church and Bishop of the Diocese of Moray, Ross & Caithness, and the Rev. Sarah Murray, Provost of Inverness Cathedral.
First Minister Humza Yousaf, Speaker of the Scottish Parliament Alison Johnstone and Highland MP Kate Forbes read at the service, which was attended by hundreds in person and streamed live.
Gaelic songs were sung by Julie Fowlis, accompanied by her husband Eamon Doorley and Ciara, a granddaughter of Mrs Ewing.
Alex Neil, a former Cabinet Secretary in the Scottish Government, also gave a eulogy, describing the impact Ms Ewing has had across the political divide, calling her “the most effective artist and activist this country has ever seen”. .
He said: “Winnie Ewing did not seek fame, fortune or honor. She just dedicated her life to fighting for freedom and independence for Scotland.”
Another of Ms Ewing’s granddaughters, Natasha, gave a short speech.
Following Ms Ewing’s death on June 21, Mr Yousaf paid tribute to the “staunch European” former MEPs and said she had “played a key role in shaping the perception of Scotland as a genuine European nation”.
Former First Minister Nicola Sturgeon said Ms Ewing, who was the first Speaker of the reconvened Scottish Parliament in 1999, was a “beloved icon”.
Mrs. Ewing is survived by her children Fergus, Annabelle and Terry and grandchildren Natasha, Ciara, Jamie and Sophie.
Her family thanked everyone who had offered their condolences and said everyone was welcome to the service.
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A family spokesman said: “We have heard countless anecdotes of happy experiences from Winnie throughout her long and fruitful career as MPs, MEPs and MSPs.
“These were a great comfort to the family.”
A private funeral service was held last month.
Born in Glasgow in 1929, Ms Ewing earned a law degree from Glasgow University before being elected to the UK Parliament.
Although she lost the Hamilton seat at the next election in 1970, she was re-elected to Westminster for Moray and Nairn in 1974 and retained her seat at the second election in October of the same year.
She also served in the European Parliament, representing the Highlands and Islands after losing her seat in Westminster in 1979.
She resigned as an MEP in 1999 to stand as a candidate for the new Scottish Parliament, where she represented the Highlands and Islands until 2003.
Ms Ewing was President of the SNP until she left elected office in 2005, but remained a fervent supporter of the independence cause.