Live 8 organiser Bob Geldof says he is confident world leaders at next week's G8 summit will listen to the call for more action to tackle global poverty.
Robbie Williams was one of the highlights of the Hyde Park concert
He said that the Live 8 day of concerts and protests had been "full of hope and possibility and life".
Chancellor Gordon Brown said it was proof "people can have power if they make their views felt".
Shows were held in 10 cities, including London, Philadelphia, Paris, Berlin, Johannesburg, Rome and Moscow.
They were designed to put pressure on the G8 leaders who are meeting next week in Gleneagles in Scotland.
Mr Brown compared the spectacular to the 1985 Live Aid concert, also organised by Geldof, to raise funds for famine relief in Ethiopia.
"In 1985 it was about charity, raising money for charity, when it was Live Aid," he said.
Geldof called for justice not charity for Africa
"Today it's about a campaign for justice and empowerment for millions of people round the world..."
Peter Mandelson, the European Union's Trade Commissioner, said the pressure had to be maintained.
"They can't ignore it," he told BBC Television. "We need to see ... that energy channeled into continuing pressure and interest and attention not just to the issues of humanitarian aid and debt relief, but trade."
Geldof said: "Mahatma Gandhi freed a continent, Martin Luther King freed a people, Nelson Mandela freed a country. It does work. They will listen."
In London, the concert was watched by 205,000 music fans who came to hear acts including Madonna, U2, Coldplay, Sir Elton John and Sting and Sir Paul McCartney and Bono.
As the 10-hour marathon concert drew to a close, Sir Paul thanked the crowd for their support to the anti-poverty campaign.
"Everybody who's come along today has come for the right reason. We hope that the people, the heads of G8 are listening hard," he said.
"They can't avoid this, they cannot have missed it and all you people who've come along for this message - we love you."
United Nations secretary-general Kofi Annan was also a guest at the London gig. He told the crowd: "This is really a united nations."
He said: "The whole world has come together in solidarity with the poor. On behalf of the poor, the voiceless and the weak, I say thank you. "
In Johannesburg, the concert was attended by 8,000 people who were entertained by mainly African acts.
The former South African President, Nelson Mandela, also appeared on stage. He said that if the G8 leaders failed to act they would be committing a crime against humanity.
"History and the generations to come will judge our leaders by the decisions they make in the coming weeks.
Bono opened the London show with Sir Paul McCartney
"I say to all those leaders: Do not look the other way, do not hesitate ... It is within your power to prevent a genocide."
Africans who knew about the global concerts thought they were a good idea but some questioned why their own musicians had been sidelined.
"What do participating musicians know about Africa?" asked Susan Outa, a student in Nairobi. "How do we know whether half of them have even visited a single African country?"
In Philadelphia, Destiny's Child, Jay Z and Bon Jovi were among the big performers, watched by a crowd of nearly one million people. And in Berlin, the Beach Boys co-founder Brian Wilson and American rockers Green Day fired up a crowd of 150,000 in Tiergarten park.
The Canadian concert in Barrie, Ontario attracted 35,000, with performers including Bryan Adams and Neil Young.
In Tokyo the concert drew around 10,000 people, all of whom were selected in a lottery.
In Rome, Faith Hill, Duran Duran and a host of Italian stars took to the stage in Rome's Circus Maximus.
After a modest start, the size of Rome's audience grew to around 200,000 by the evening, police said, although organisers had been hoping for up to one million people.
Italy's singing stars did not attract the number of people hoped for
The Italian media said a combination of the summer heat, annual holidays, plus the draw of watching the other worldwide events at home on television, might have caused a lower turn-out than expected.
Some of the artists also said the mainly home-grown line-up for the Rome concert was less attractive than the global stars, such as the Pink Floyd, who were playing in London.
"I'm sure they all went to see Pink Floyd in London," said Cesare Cremonini, one of the stars at the Rome concert.
"I, too, would probably have wondered whether it was better to go to Rome to see Cremonini or to London to see Pink Floyd."
Elsewhere, the Paris concert attracted 100,000 and a concert of African artists at the Eden Project, on the UK's south west coast, drew a capacity 5,000-strong crowd.