World leaders and joyous, singing South Africans have honoured Nelson Mandela at a Soweto soccer stadium that was two-thirds full amid cold, driving rain.
The crowds booed South African President Jacob Zuma, who was to give the keynote address at the service, which started an hour late.
Crowds converged on FNB Stadium in Soweto, the Johannesburg township that was a stronghold of support for the anti-apartheid struggle that Mandela embodied as a prisoner of white rule for 27 years and then during a peril-fraught transition to the all-race elections that made him president.
Steady rain kept many people away. The 95,000-capacity stadium was filling up during the ceremony, which began at noon local time with the singing of the national anthem.
The mood was celebratory. A dazzling mix of royalty, statesmen and celebrities was in attendance.
The service heard from family friend Andrew Mlangeni, a former prisoner on Robben Island with Mandela, who spoke of the "outpouring of love" following his death.
"Madiba is looking down on us. There is no doubt he is smiling and he watches his beloved country, men and women, unite to celebrate his life and legacy," he said.
Thabo Mbeki, the former South African president who succeeded Mandela, got a rousing cheer as he entered the stands while Zimbabwe's President Robert Mugabe was booed.
French President Francois Hollande and his predecessor and rival, Nicolas Sarkozy, arrived together. United Nations Secretary-General Ban Ki-moon waved and bowed to spectators who sang praise for Mandela, seen by many South Africans as the father of the nation.
Mandela's widow, Graca Machel, and former wife Winnie Madikizela-Mandela were at the stadium, and gave each other a long hug before the ceremonies began. So were actress Charlize Theron, model Naomi Campbell and singer Bono.
US President Barack Obama was greeted by loud cheers after arriving late at the memorial service, as UN Secretary-General Ban Ki-moon was speaking.
In his tribute, Ban said the world had lost a mentor.
"We join together in sorrow for a mighty loss and the celebration of a mighty life," he said.
"Nelson Mandela was more than one of the greatest leaders of our time, he was one of our greatest teachers. He taught by example, he sacrificed so much and was willing to give up everything for freedom, equality and justice.
"His compassion stands out most," Ban said.
The UN secretary-general was followed by the chair of the African Union, Dr Nkosazana Dlamini-Zuma.
She was followed by Obama, who shook hands with President Raul Castro of Cuba as he took his place on stage.
Obama received a rapturous welcome when he took the podium.
"It is hard to eulogise any man ... how much harder to do so for a giant of history, who moved a nation towards justice," Obama said.
He told South Africans: "The world thanks you for sharing Nelson Mandela with us. His struggle was your struggle, his triumph, your triumph."
He praised Mandela as the last great liberator of the 20th century.
"We learned so much from him and we can learn from him still... He showed us the power of action, of taking risks."
The president, who flew 16 hours to the ceremony, also took a swipe at authoritarian leaders and enemies of the US who claim to embrace Mandela's legacy but did not act upon it.
"There are too many leaders who claim solidarity with Madiba's struggle for freedom, but do not tolerate dissent from their own people," he said, in a comment that might have been aimed at Cuban leader Raul Castro, who was to follow him on the roster of speakers.
Brazilian President Dilma Rousseff said: "He also was a source of inspiration for similar struggles in Brazil and across South America. His fight reached way beyond his nation's border and inspired young men and women to fight for independence and social justice."
China's Vice President Li Yuanchao said through a translator: "Mr Mandela was the pride of the African people. He has dedicated his entire life to the development and progress of the African content."
The sounds of horns and cheering filled the stadium. The rain, seen as a blessing among South Africa's majority black population, enthused the crowd.
"In our culture the rain is a blessing," said Harry Tshabalala, a driver for the justice ministry. "Only great, great people are memorialised with it. Rain is life. This is perfect weather for us on this occasion."
"It is a moment of sadness celebrated by song and dance, which is what we South Africans do," said Xolisa Madywabe, CEO of a South African investment firm.
