US President Barack Obama is welcomed by a huge cheer from the crowd as he begins his speech, in which he describes Mr Mandela as a "giant of history", adding: "The world thanks you for sharing Nelson Mandela with us."
On his way to the podium, President Obama shakes hands with Cuban President Raul Castro, an unprecedented gesture between the leaders of two nations that have been at loggerheads for more than half a century.
There were some boos for current South African President Jacob Zuma, but his keynote address was respectfully heard. He said Mr Mandela had been "one of a kind... a fearless freedom fighter who refused to allow the brutality of the apartheid state to stand in way of the struggle for the liberation of his people".
John Simpson, the BBC's World Affairs Editor said: "Despite the difficulties - the driving rain and logistical challenges - of organising this event, it must remain a source of immense pride for South Africans that a memorial for one of their own has attracted such an array of world dignitaries
Nelson Mandela's widow Graca Machel listens to the tributes including that by UN Secretary General Ban Ki-moon who said: "Mandela hated hatred. Not the people. He showed wholesome power of forgiveness. A unique gift."
The heavy rain continued as deputy president of the ANC Cyril Ramaphosa addressed the crowd and welcomed those in the stadium and those watching around South Africa and around the world. He said: "In our tradition, when it rains when you are buried, your gods are welcoming you to heaven."
South Africa's Archbishop Emeritus Desmond Tutu, a leading figure in the struggle against apartheid earlier said of Mandela: "He was a unifier from the moment he walked out of prison. We are relieved that his suffering is over, but our relief is drowned by our grief."
Since Mandela's death, Johannesburg has been blanketed in unseasonal cloud and rain but despite this the atmosphere inside the stadium was one of joy and celebration.
As the time for the ceremony to start draws near some of the dignitaries arrive, including South Africa's last white president FW De Klerk with his wife Elita.
Alongside the politicians a number of figures from the world of entertainment attended the ceremony, including U2's lead singer Bono and South African actress Charlize Theron
The former South African president died aged 95 last Thursday and the country is observing a series of commemorations leading up to the funeral on Sunday
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