South African President Jacob Zuma said "the nation has lost its greatest son", adding: "He is now resting. He is now at peace." "Our people have lost a father," said Mr Zuma.
"Although we knew this day was going to come, nothing can diminish our sense of a profound and enduring loss.
"His tireless struggle for freedom earned him the respect of the world. His humility, passion and humanity, earned him their love."
UK Prime Minister David Cameron, speaking outside Downing Street, said: "Tonight one of the brightest lights of our world has gone out.
"Nelson Mandela was not just a hero of our time, but a hero of all time.
"Through his dignity, through his triumph, (he) inspired millions."
"He achieved more than can be expected of any man - and today he's gone home," said President Obama.
"We've lost one of the most influential, courageous and profoundly good human beings that any of us will share time with on this earth."
"He no longer belongs to us - he belongs to the ages."
The Queen said she was "deeply saddened" by Nelson Mandela's death, saying he "worked tirelessly for the good of his country, and his legacy is the peaceful South Africa we see today".
South Africa's archbishop emeritus Desmond Tutu said South Africa was "drowned by grief".
"He was a unifier from the moment he walked out of prison," he said.
Former Irish president Mary Robinson "As we mourn the passing of this extraordinary man, and young people around the world feel a particular sense of loss, we can honour him best by giving of ourselves to others."
French President Francois Hollande added: "Nelson Mandela's message will not disappear. It will continue to inspire fighters for freedom, and to give confidence to peoples in the defence of just causes and universal rights."
Australian Prime Minister Tony Abbott said: "He spent much of his life standing against the injustice of apartheid.
"When that fight was won, he inspired us again by his capacity to forgive and reconcile his country.
"While the world may never see another Nelson Mandela, he has inspired countless men and women throughout the world to live more courageous and honest lives."
Scotland's First Minister Alex Salmond described him as a "towering statesman" whose influence "transcended ideology, race and creed".
UN Secretary General Ban Ki Moon said: "Only because of such a great man like Nelson Mandela is it possible that particular people in Africa and elsewhere are able to enjoy freedom and human dignity."We have to learn the wisdom and determinations and commitment of Mr Mandela to make this world better for all."
US Secretary of State John Kerry said: "Now that his long walk has ended, the example he set for all humanity lives on. He will be remembered as a pioneer for peace."
A joint message from President of the European Commission, Jose Manuel Barroso, and President of the European Council, Herman Van Rompuy, said: "We mourn the death of one of the greatest political figures of our times.
"Nelson Mandela represents the fight against racism, political violence and intolerance. Only a person with his profound humanity, moral integrity and authority and clear vision for the future of his country, could have achieved this."
Israeli Prime Minister Benjamin Netanyahu said he was the "father of his people", adding: "He will be remembered as the father of new South Africa and as an outstanding moral leader."
German Chancellor Angela Merkel said: "Nelson Mandela's shining example and his political legacy of non-violence and the condemnation of all forms of racism will continue to inspire people around the world for many years to come.
Russian President Vladimir Putin described Mr Mandela as "one of the greatest politicians in modern times", saying the former South African leader was a man who never betrayed his convictions.
"Mandela, having gone through the most difficult ordeals, was committed to the end of his days to the ideals of humanism and justice," Mr Putin was quoted as saying in a statement