Speaking shortly after the death of the civil rights leader was announced, Mr Obama said now is the time for people to pause and honor the fact 'that Nelson Mandela lived.
He said: 'Like so many around the globe, I cannot fully imagine my life without the example that Nelson Mandela set.'
'He no longer belongs to us - he belongs to the ages,' Mr Obama said from the White House briefing room.
The Queen has said she is 'deeply saddened' to learn of Nelson Mandela's death, saying the former South African president 'worked tirelessly for the good of his country'.A statement from Buckingham Palace said: 'The Queen was deeply saddened to learn of the death of Nelson Mandela last night. He worked tirelessly for the good of his country, and his legacy is the peaceful South Africa we see today.
'Her Majesty remembers with great warmth her meetings with Mr Mandela and sends her sincere condolences to his family and the people of South Africa at this very sad time.'
The Prince of Wales also paid tribute to the former South African leader.He said: 'Mr Mandela was the embodiment of courage and reconciliation. He was also a man of great humour and had a real zest for life.
'With his passing, there will be an immense void not only in his family's lives, but also in those of all South Africans and the many others whose lives have been changed through his fight for peace, justice and freedom.
'The world has lost an inspired leader and a great man. My family and I are profoundly saddened and our thoughts and prayers are with his family.'
Prime Minister David Cameron said: 'Nelson Mandela showed us the true meaning of courage, hope, and reconciliation.'
'My heart goes out to his family - and to all in South Africa and around the world whose lives were changed through his courage.'
Cameron tweeted that the flag at No 10 Downing Street would be flown at half-mast.
'A great light has gone out in the world,' Cameron said. 'Nelson Mandela was a hero of out time.
Deputy Prime Minister Nick Clegg said: 'Every so often history produces an individual whose message is universal, and Nelson Mandela will be mourned and missed on every continent around the globe.'
Labour leader Ed Miliband called his work to unite South Africa in the face of personal hardship and oppression 'extraordinary'.
He said: 'The world has lost the inspirational figure of our age. Nelson Mandela taught people across the globe the true meaning of courage, strength, hope and reconciliation.'
Foreign Secretary William Hague said Mr Mandela's life story is 'a compelling and inspiringly profound political journey'.
Former prime minister Tony Blair said the political leader was 'great man' who had made racism 'not just immoral but stupid', while former prime minister Gordon Brown called Mr Mandela 'the greatest leader of our generation'.
Former South African president F.W. de Klerk, who was the last white president of the country before Mandela came to power, had nothing but praise for the 'father' of the country.
'He made reconciliation happen in South Africa,' Mr de Klerk told CNN
'There was an immediate I would say a spark between the two of us.
'I always respected him and I always liked him as a person he was a magnanimous person, he was a compassionate person.
Mandela's South African comrade Desmond Tutu, the first black Archbishop of Cape Town, wrote an article on his friend's passing, saying that the world was a better place because of Mandela.
'He was not only an amazing gift to humankind, he made South Africans and Africans feel good about being who we are. He made us walk tall,' Mr Tutu said.
Echoing Mr Obama's speech, all of the living U.S. presidents made statements of their own about Mandela.
Bill Clinton, who met with Mandela on a number of occasions and grew close with the elderly leader, released a statement on behalf of his family.
Today the world has lost one of its most important leaders and one of the finest human beings,' who was 'a champion for human dignity'.
'He proved that there is freedom in forgiving, that a free heart is bigger than a closed mind.'
Mr Mandela came to America to attend President Clinton's inauguration in 1994 and Mr Clinton visited the ailing leader earlier this year.
Madeline Albright, Clinton's secretary of state, issued a statement of her own saying Mandela 'taught us all that forgiveness is stronger than hate. The best way to honor his passing is to follow his example'.
Both Bush presidents reacted to the death of the African leader.
