Image source, Getty Images

Nelson Mandela was the father of the nation, Mr Ramaphosa says.

His sacrifices touched the lives of millions, and will inspire many generations to come, he adds.

"He led us from the wilderness of conflict and oppression into the land of peace and freedom," Mr Ramaphosa continued.

His vision "crossed borders" and "spanned continents", Mr Ramaphosa continued.

"He is hailed as a global icon; he is memorialised in towering statues in many parts of the world; his likeness adorns our currency.

"Yet his most enduring accomplishment was to teach us what it means to be a human."

The Duke and Duchess of Sussex have met Nelson Mandela's granddaughter Zamaswazi Dlamini-Mandela at an exhibition in London paying tribute to his life.

Here is the Duchess chatting to Ms Dlamini-Mandela:

Image source, PA

You can read all about their visit - and the exhibition in central London - on BBC News: Harry and Meghan visit Mandela exhibition in London

President Cyril Ramaphosa says South Africans are "truly humbled and privileged" to be celebrating the centenary of the birth of Nelson Mandela.

Many are attending the Mandela lecture because Barack Obama had agreed to deliver it, he adds.

Mr Ramaphosa has received a huge applause. The crowd is on its feet. It has burst out in song.

Image source, AFP

Graca Machel has ended her speech. She receives applause from the crowd - and a kiss from Barack Obama.

Next speaker - Cyril Ramaphosa who will introduce Mr Obama.

... They are running a little behind schedule in Johannesburg, so we aren't too sure when Barack Obama will actually start speaking.

It should have been 30 minutes ago.

Graca Machel's words have delighted people on Twitter:

Graca Machel says Barack Obama was an inspiring symbol - like Nelson Mandela.

Both were symbols of victory over adversity, she says.

Mr Obama stands on the shoulders of giants, she adds.

Graca Machel has continued to give a glimpse into her husband's character.

He knew he was "a flawed human being and said on many occasions he was not a saint", she told the crowd, and even his worldwide fame did not shake him "into pompous arrogance".

"The essence of who he was and his level of self-awareness had never been altered. His sober view of himself... many times he would say 'I am a country boy'," she said.

Ms Machel also pointed to the fact he looked to the future generations to complete what he had started.

Quoting from Long Walk to Freedom, his autobiography, she said: "The truth is that we are not yet free. We have merely achieved the freedom to be free... We have not taken the final step of our journey, but the first step."

Some people are getting impatient as Graca Machel pays tribute to her late husband - they want to hear Barack Obama.

Image source, AFP

Graca Machel has taken pains to point out, while her late husband became a symbol of the struggle against the racist system of apartheid, he never saw himself as such.

"He was not acting in singular isolation," she told the crowd. "He considered himself a simple foot solider."

She reminded the crowd of his words as he left prison in 1990: "I stand here before you, not as a prophet, but as a humble servant of you the people."

She added: "The Madiba I know is a simple, grounded and humble man."

Graca Machel is now speaking. She says she is thrilled that Mr Obama is in South Africa to deliver the keynote speech at the Mandela lecture.

Here's a photo of Mr Obama, waving at the crowd at the packed Wanderers stadium:

Image source, Reuters

Patrice Motsepe has called for an end to corruption in South Africa

The "initiators of corruption" are often business people, he says, adding there should be "zero tolerance" for it.

South Africa's richest black businessman, Patrice Motsepe, is speaking ahead of Barack Obama's Nelson Mandela lecture.

He said he shed a tear when both Mr Mandela and Mr Obama were inaugurated as the first black president of their countries.

Mr Motsepe also gave a warm welcome to the former US leader:

Here's a photo of Barack Obama with Mr Mandela's widow, Graca Machel:

Image source, Reuters

Professor Njabulo Ndebele has told the crowd in Johannesburg Barack Obama was chosen because he "has things to tell us which are worth listening to".

He concluded his welcome by urging the crowd: "Let us find the Madiba in each of us. Let us be the legacy."

His words have gone down well:

Mr Obama was a leader who sought to renew hope and optimism, Professor Njabulo Ndebele says.

He has confronted global challenges in a way few have, he adds.

Zapiro, arguably South Africa's most famous cartoonist, has shared this drawing from 2013, when Barack Obama gave a speech at Mandela's memorial:

You can read what we wrote about that speech by clicking here, or watch the speech in full here.

This is the most popular Nelson Mandela lecture since they began 16 years ago.

It is thought they are as many as 15,000 people packed into the stadium, fulfilling a dream of the late Ahmed Kathrada, one of the foundation's founding trustees who spent almost 30 years in jail with Mr Mandela, according to Professor Njabulo Ndebele.

And it is as popular outside the stadium as it is within it: here is the list of the top Twitter trends in South Africa: