Mr Mandela, the iconic anti-apartheid revolutionary and the first black president of South Africa, died on Thursday night following a long period of ill-health.
The 95-year-old ailing former leader had retired from public life almost a decade ago, having been vulnerable to respiratory problems since contracting tuberculosis during his 27 years of incarceration.
Madiba, as he was affectionately known, passed away peacefully surrounded by family members at his Johannesburg home where he had been receiving medical treatment for a lung infection.
On hearing of his death, South Africans crowded outside his home singing in tribute throughout the night.
In London, his daughters Zindzi and Zenani Mandela had been attending the premiere of a film chronicling his life when the news broke.
The film's star Idris Elba, who plays Mr Mandela, and producer Harvey Weinstein joined the audience for a moment's silence in his honour.
Current South African President Jacob Zuma has confirmed that Mr Mandela's body will lie in state for three days before a funeral is held on Sunday 15 December in Qunu, the village in where he was born.
Books of condolence have already opened in towns and cities around the world.
Nelson Mandela carried out his role with a real talent to draw people and whole communities together. South Africa and the rest of the world had a tremendous respect for him.
Northern Ireland's leaders, who are returning from a trade mission in Japan, have expressed their profound sadness at his loss.
Mr Mandela was a supporter of the peace process in Northern Ireland and met with many key figures since his release from prison.
Mr Robinson said: "It is with deep sorrow that I heard of the death of Nelson Mandela and I offer my condolences to his entire family circle at this time.
"We have known for some time that he was ill, nonetheless, it still comes as a great shock to lose such an inspirational man and a massive figure in terms of world politics.
The First Minister said he was struck by Mr Mandela's "considerable humility and charisma" when he met with him on two occasions.
"He did not see himself in terms of celebrity yet barely anyone throughout the world would not recognise his name and that is no small part because of his unique ability to connect personally with people," Mr Robinson commented.
"When I asked how he dealt with opposition and the business of negotiation he commented that real negotiation is not with political opponents, rather with your own community and while they may feel you are stepping ahead of them, it is important to convince them to make the journey - a message so pertinent to our own peace process."
Nelson Mandela was a true friend to Ireland.
Mr McGuinness offered heartfelt sympathies to the family of the former South African leader.
"I was honoured to meet Nelson Mandela the last time he was in Dublin and there is no doubt he was truly one of the greatest leaders of our lifetime," the Sinn Féin senior figure said.
He said it was appropriate that Mandela was recognised with the Nobel Peace Prize in 1993.
"He will be remembered for demonstrating what is possible when people are committed to peace and reconciliation in areas of conflict. Nelson Mandela has left an indelible mark not only in South Africa but across the world," Mr McGuinness continued.
In 1997, at the invitation of President Mandela, the Sinn Féin MLA led a delegation to South Africa for significant peace talks.
The deputy First Minister commented: "President Mandela's interest in the success of the peace process was epitomised by the valuable contributions made by amongst others Cyril Ramaphosa, his Chief negotiator and the nowDeputy President of African National Congress, who was a constant source of support to us throughout."
He was revered through his life and will be remembered in death as one of the greatest ever campaigners for peace, justice and reconciliation. He touched Northern Ireland in many ways and provided real inspiration to the peace process. His legacy should remind us that division can be overcome and a shared future is possible.
Theresa Villiers, Secretary of State for Northern Ireland
Nationalist and unionist politicians have united as they paid tribute to Mandela.
SDLP leader Alasdair McDonnell said: "His enduring legacy will be one of hope, even in the most difficult of circumstances. That sentiment unites us all."
UUP leader Mike Nesbitt said: "As President his respect for others and his humanity was an inspiration to all and helped smooth South Africa's transition to democracy. He was an iconic figure and a symbol of hope for many people throughout the world."
Alliance Leader David Ford MLA said Mr Mandela would be missed by millions of people.
He said: "I remember a quote by him which has particular relevance to Northern Ireland - 'No one is born hating another person because of the colour of his skin, or his background, or his religion.
"'People must learn to hate, and if they can learn to hate, they can be taught to love. For love comes more naturally to the human heart than its opposite'."
Tributes to the 95-year-old, who is being remembered as the most respected political leader of all time, have been made around the globe.
This is a celebration of Nelson Mandela’s life and of the lives that ordinary South Africans have been able to lead because of the sacrifice he made.
ITV’s Rohit Kachroo, in Johannesburg
The Queen said she is "deeply saddened" to learn of Mr Mandela's death, saying he "worked tirelessly for the good of his country".
Taoiseach Enda Kenny asked for his spirit to continue to inspire, guide and enlighten others.
US President Barack Obama said the world has lost an influential, courageous and "profoundly good" man.
Mr Obama added: "Madiba transformed South Africa and moved all of us.
"He achieved more than can be expected of any one man. I cannot imagine my own life without Mandela's example and so long as I live, I will do what I can to learn from him."
Prime Minister David Cameron said "a great light has gone out in the world".
He continued: "Nelson Mandela was a towering figure in our time; a legend in life and now in death - a true global hero.
"My heart goes out to his family - and to all in South Africa and around the world whose lives were changed through his courage."
A book of condolence for Nelson Mandela will be available at Belfast City Hall on Friday afternoon. City Hall will also be open on Saturday and Sunday, from 9.30am to 4pm, for those wishing to pay their respects.