Nelson Mandela Place, near Buchanan Street, was closed off yesterday afternoon to allow mourners to pay their respects.
Politicians and activists from across Scotland gathered less than 24 hours after the announcement of his death, and spoke of the statesman's life, impact and relationship with Glasgow and the rest of Scotland.
Glasgow City Council leader Gordon Matheson was joined by Glasgow Central MP Anas Sarwar and Humza Yousaf, Scottish Minister for External Affairs and International Development.
Brian Filling, the anti-apartheid activist who arranged for Mandela to visit Glasgow to be awarded the freedom of the city, also addressed the crowd, who shouted "Viva Mandela" in response.
Sonwabiso Ntonga, 20, a student from South Africa, now lives in Glasgow but she remembers visiting Mandela with her cousin at the age of four.
"My uncle was friends with him so we went to his house when I was little," she said. "He was very welcoming, and he gave my cousin and me a drink - we were so excited to be there.
"I came here to remember him, all of the great things he has done.
"As a South African, it is important to be here to support him, and also knowing the history of Glasgow with South Africa, I thought it was a duty of mine to come and represent the people of South Africa and my family."
Ms Ntonga was joined by her friend Helen Wanjiru, 20, a student who also lives in Glasgow.
Ms Wanjiru said: "He was a great man, one of the great heroes of the world and I'm here to pay tribute to his bravery."
People from all over the country came to the packed city centre square to pay their respects, and many wept as music was played by Arthur Johnstone and the Stars band.
Gerry McCulloch, a retired English teacher from Saltcoats, said: "I was in Durban some years ago and I saw firsthand the impact that Mandela made there. I was part of a Scottish delegation of teachers and we went to look at the black township schools there.
"I can't think of any living politician who would be accorded this kind of universal praise."
Joshua Martin, 27, an arts director from London, was visiting Glasgow yesterday and decided to join the service.
"I wanted to be part of the memorial for a great man who did a lot for people with Aids," said Mr Martin. "I don't think we'll ever have another man quite like him, and I think the world is a lot richer for knowing him.
Sal Bennett, 45, an upholsterer from Broomhill who attended the Free Nelson Mandela event 18 months before Mandela was freed, joined the vigil with her son Shay and his friend Saami, both 11.
Ms Bennett said: "I think it's a really important, significant thing to recognise and to teach my children; I think it's vital that they know about Mandela."
Outside Scottish Government headquarters at St Andrew's House in Edinburgh, the South African national flag flew at half-mast alongside the Saltire and condolence books were opened at several council centres across the country.
Tributes continued to pour in from charities, campaigners and politicians, with Mandela's links with different universities and cities recognised and remembered.
He was elected honorary member of the students' association at the universities of Glasgow and Strathclyde in 1984, the same year he was awarded the Freedom of the City of Aberdeen.
In 1990, Glasgow Caledonian University was the first to award him an honorary doctorate on his release from prison.
He was granted Freedom of the City of Edinburgh in 1997.
He had been patron of the Scottish Refugee Council since 1995. Judith Robertson, chair of the board of directors, said the charity would continue to take "hope, inspiration and dignity" from his life.
Professor Alan Miller, chairman of sthe Scottish Human Rights Commission, said Mandela transcended race, class and nationality to "bring out the best in all of us".
Dr Michael Kelly was Lord Provost of Glasgow in 1981 when the city became the first to honour Mandela with the Freedom of the City.
He said the mood at the time was not as it is now and he had to convince people to support the award. When Mandela came to Glasgow in 1993 he told Dr Kelly that hearing of the support he had in Scotland, and across the world, had given him great encouragement.
"I think he will be remembered as a man whose life was fulfilled," he said. "He set out with a political ambition to change society and despite extreme difficulties in his life he was able to die knowing he had achieved that. It's a fulfilled life."