The relationship achieved a degree of worldwide fame when, in 1981, the city awarded Mandela the freedom of Glasgow.
At the time, he was still in jail, courtesy of the white South African regime. Mandela would later say that Glasgow's decision reminded him the world had not forgotten the ANC's struggle.
He was finally freed in February 1990, walking out of Victor-Verster Prison into a global media whirlwind, a free man for the first time in nigh on three decades.
A visit to Glasgow was arranged for February 1993, prompting councillor Jean McFadden, then leader of the Labour-controlled council, to say: "Mr Mandela is coming here to be honoured, but the honour is ours. He is a symbol of the fight for equality and freedom throughout the world."
The trip was cancelled on doctors' orders, but the indefatigable Mandela finally arrived here that October.
The day the 75-year-old statesman arrived, it was the only show in town. Not even the rain could dampen the overwhelming sense of occasion in George Square, which lay within sight of Nelson Mandela Place, the street re-named in his honour in 1986.
Ordinary Glaswegians, students and activists with ANC banners, Labour MPs, pensioners, young couples, all were drawn to the Square.
"He did not smile: he positively beamed," a report in The Herald noted. "His eyes, no longer haunted by his years in prison, sparkled with mischief and humour."
Mandela himself said: "People of Glasgow, I am now free to be with you. I am free and I am here today to thank you. But I am still denied the most fundamental of freedoms in my own country - the right to vote. But I bring a message of hope. We have made great progress towards our goal of one person, one vote."
He earned a huge cheer when he said that right would prevail in South Africa "because there are men and women who regard the whole world as the theatre of their efforts and their battlefield".
Watched by veteran anti-apartheid campaigner Archbishop Trevor Huddleston, Mandela held the hand of 14-year-old Glasgow schoolgirl Lesley Paterson, who had won a competition in The Herald's sister paper, the Evening Times, to meet him.
"We want young people like her,'' he told the crowd. "No cause can fail if it is supported by the youth, and that is something to which she has responded.''
The youngster, needless to say, was awestruck. "It was great," she managed to say. "He was fantastic.''
Mandela delighted the crowd by dancing with a South African singer, Mara Louw, as she sang a Sowetan pop song called Turn Me Around.
At the end, he left the stage and plunged into the cheering throng: a never-to-be-forgotten moment for those who were fortunate enough to be there.
Earlier in the day, at a more formal ceremony in the City Chambers, Mandela had met some 400 dignitaries and guests, representing not only Glasgow but all the other towns and cities that had offered him their freedom, including Aberdeen, Midlothian and Dundee.
Declaring that Glasgow would always enjoy a distinguished place in the records of the international campaign against apartheid, he went on: 'The people of Glasgow were the first in the world to confer on me the Freedom of the City at a time when I and my comrades in the ANC were imprisoned on Robben Island serving life sentences which, in apartheid South Africa, then meant imprisonment until death.''
That year was an important one for Mandela: not only was he able to visit Britain, but he also received the Nobel Peace Prize, alongside FW de Klerk, then president of South Africa.
In June 2002, Mandela, by now the former President of his country, was here again: back in Glasgow, but this time, a few miles to the east of George Square.
At Barlinnie Prison, he spent an hour with Abdelbaset Ali Mohmed al Megrahi, the man who had been convicted of the Lockerbie bombing.
Mandela later met families of some of the Lockerbie dead.
In August 2009, in the wake of the Scottish Government's controversial decision to free the terminally ill Al Megrahi, he expressed his appreciation.
Professor Jake Gerwel, chairman of the Mandela Foundation, said: "Mr Mandela sincerely appreciates the decision to release Mr al-Megrahi on compassionate grounds."
First Minister Alex Salmond responded: "We have seen today that Nelson Mandela has come out firmly in support, not just as the towering figure of humanitarian concern, but of course somebody who brokered the agreement that led to the Lockerbie trial in the first place.
"Many people believe that you will achieve more in this world through acts of mercy than you will through acts of retribution."
There is one last footnote to that day in George Square in 1993: in 2010, when Billy Connolly was made a Freeman of the City of Glasgow, Nelson Mandela sent a personal message, saying: "I wish Mr Connolly my congratulations at the high honour being bestowed on him. Welcome to a very special club indeed!"