Nelson Mandela's body has now been taken to a military hospital in Pretoria.
South Africa's first black President will receive a full state funeral and flags will remain at half-mast until after the burial.
Archbishop Desmond Tutu, who like Mandela campaigned against apartheid, says Nelson Mandela transcended race and class.
Melanie Verwoerd was a member of parliament for the ANC party during the first democratic elections in South Africa in 1994.
The former South African Ambassador to Ireland says her country would have been a very different place if it weren't for Mandela.
Taoiseach Enda Kenny has described the death of former South African President Nelson Mandela as ``a great light extinguished''.
“The name Mandela stirred our conscience and our hearts. It became synonymous with the pursuit of dignity and freedom across the globe,” Mr Kenny said.
The Taoiseach said Mr Mandela changed life in South Africa, and humanity.
“As we mark his passing, we give thanks for the gift of Nelson Mandela. We ask that his spirit continues to inspire, guide and enlighten us as we strive to bring freedom and dignity to the family of man, our brothers and sisters, across the world,” he said.
“I offer my deepest sympathies, on behalf of the Irish Government and people, to his family, to his friends and supporters, and to the Government and the people of South Africa.”
President Michael D. Higgins said it was "with deepest sadness" that he had learned of the death of Mandela.
"On behalf of the people of Ireland, I offer sincere condolences to his family and the people of South Africa," he said in a statement.
"Nelson Mandela is one of history’s greatest leaders; a man whose unprecedented courage and dedication broke down the cruel barriers of apartheid in South Africa and led the nation into a new and democratic age."
Bono said Nelson Mandela was stubborn until the end for all the right reasons - but last night he finally blinked.
In a statement, the U2 singer said it was if the South African leader was born to teach the age a lesson in humility, humour and above all else, patience.
He said: "Some of us cry, knowing our eyes were opened to so much because of him."
UK Prime Minister David Cameron said “a great light has gone out in the world”.
The flag at No 10 will be flown at half-mast in honour of the former leader, who was a “hero of our time”, the Prime Minister said.
"Courage ...not the absence of fear, but the triumph over it." The world gives thanks for a life of courage. pic.twitter.com/175B95XR3Y— Salman Rushdie (@SalmanRushdie) December 5, 2013
US president Barack Obama said the world has lost an influential, courageous and ``profoundly good'' man.
Mr Obama said Mandela “no longer belongs to us. He belongs to the ages.”
Speaking from the White House, Mr Obama said he was one of the countless millions around the world who was influenced by Mandela.
He met Mr Mandela’s family earlier this year when he visited South Africa. But he did not meet the ailing leader, who was in hospital throughout his visit.
Mr Obama added that the former South African leader represented the fight for freedom and dignity throughout the world.
He said: “Madiba transformed South Africa and moved all of us. His journey from a prisoner to a president embodied the promise that human beings and countries can change for the better.
“His commitment to transfer power and reconcile with those who jailed him set an example all humanity should aspire to, whether in the lives of nations all our own personal ones.”
“He achieved more than can be expected of any one man.”
He added: “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.”
UN secretary-general Ban Ki-moon said Nelson Mandela was “a giant for justice” whose “selfless struggle for human dignity, equality and freedom” inspired many people around the world.
“No one did more in our time to advance the values and aspirations of the United Nations,” he said.
“Nelson Mandela showed what is possible for our world, and within each one of us, if we believe a dream and work together for justice and humanity. Let us continue each day to be inspired by Nelson Mandela’s lifelong example to keep working for a better and more just world.”
The UN Security Council interrupted a meeting on the tribunals for former Yugoslavia and Rwanda and stood for a minute in silent tribute to Mandela.
Former US president Bill Clinton said: ``Today the world has lost one of its most important leaders and one of its finest human beings. And Hillary, Chelsea and I have lost a true friend.
“History will remember Nelson Mandela as a champion for human dignity and freedom, for peace and reconciliation.
“We will remember him as a man of uncommon grace and compassion, for whom abandoning bitterness and embracing adversaries was not just a political strategy but a way of life.
“Our thoughts and prayers go out to Graca and his family and to the people of South Africa.
“All of us are living in a better world because of the life that Madiba lived.
“He proved that there is freedom in forgiving, that a big heart is better than a closed mind, and that life’s real victories must be shared.”
Every time Melinda and I met Nelson Mandela, we left more inspired than ever. His grace and courage changed the world. This is a sad day.— Bill Gates (@BillGates) December 5, 2013
In a statement, former US president George W Bush said: ``President Mandela was one of the great forces for freedom and equality of our time.
“He bore his burdens with dignity and grace, and our world is better off because of his example.
“This good man will be missed, but his contributions will live on forever. Laura and I send our heartfelt sympathy to President Mandela’s family and to the citizens of the nation he loved.”
American civil rights leader Jesse Jackson said Mr Mandela's ``imprint'' would be ``everlasting''.
“My heart weighs heavy,” said Mr Jackson, who has been in the UK this week and spoke to students in Cambridge on Monday. “The imprint he left on our world is everlasting.”