The President of the Hellenic Olympic Committee, Spyros Capralos, passed the flame to Princess Anne, president of the British Olympic Association in the Panathenaic Stadium.
Lit in Olympia on 10 May, the flame was taken on a week-long tour of Greece.
A British delegation including David Beckham are due to fly with the torch to the UK on Friday.
It will then be carried 8,000 miles (12,875 km) by 8,000 bearers in a 70-day relay ending at the Olympic Park.
The relay begins at Land’s End on Saturday when triple Olympic sailing champion Ben Ainslie will be the first to carry the torch on British soil.
After criss-crossing every region of the UK, the flame will be used to light the cauldron in Stratford’s Olympic Stadium at the opening ceremony of the Olympic Games on 27 July.
At Thursday’s handover ceremony, crowds in the stadium stood beneath multi-colored umbrellas as the national anthems of the UK and Greece were sung by a British school choir and a Greek tenor.
Heavy rain abated and a rainbow could be seen as the flame was carried into the Panathenaic Stadium – host of the first modern Olympic Games in 1896 – by Christina Giazitzidou, Greece’s world champion in rowing, who held aloft an olive branch of peace in her free hand.
Celebrated athletes carried the flame around the athletics track in a relay before the final torchbearers, Greek weightlifter Pyrros Dimas and Chinese gymnast Li Ning – who lit the Olympic cauldron at Beijing 2008 – lit the cauldron in the centre of the stadium, formally ending the Greek leg of the relay.
The British delegation included London 2012 chief Lord Sebastian Coe, Olympics Minister Hugh Robertson and London Mayor Boris Johnson.
Lord Coe told the thousands-strong crowd that millions of people across the UK were working to get the UK ready to welcome the world, and said the torch would touch every region of the nation on its 70-day relay.
“The story of the flame will be about those that carry it – their stories will inspire,” he said.
Princess Anne said earlier the relay was likely to stoke excitement for the Games in the UK, as it had in Canada ahead of the Vancouver Winter Olympics.
“When the flame arrives and the torch relay starts to get under way, that is a physical moment in terms of the process towards the Games.
“Certainly in Canada they were amazed by the effect that that had and I think that may well be true for Britain as well.”
Boris Johnson said the torch relay democratized the Olympic experience.
“It’s lighting the touch paper of a 70-day fuse that will then go off in the great pyrotechnics of the opening ceremony,” he said.
Boris Johnson said the key tests for London 2012 were both whether the Games were well-received, and whether they left a legacy for London and the UK.
Hugh Robertson accepted that putting on the Games was a huge responsibility, but said if London 2012 was a success it would be a great advertisement for both London and the UK.
Also attending the ceremony were London 2012 ambassador David Beckham and five young people chosen by Games organizers LOCOG and the British Council for their commitment to sport and their role in promoting the Olympic values of friendship, excellence and respect within their school or college.
Hailing from different national regions, the youngsters are part of London 2012’s Get Set education network and school linking programmes run by the British Council.
After spending Thursday night at the British embassy in Athens, the flame will be brought to the UK by the British delegation on BA2012 on Friday evening, where there will be a welcoming ceremony at RNAS Culdrose in Cornwall.
The flame – symbolizing purity because it comes directly from the sun – was kindled at a 10 May ceremony in Olympia by actress Ino Menegaki, playing a high priestess, who caught the sun’s rays in a parabolic mirror.
That ceremony took place amid the Temple of Hera ruins, by the ancient Olympic Games stadium.
The torch was then carried 1,800 miles through Greece by 500 torchbearers on a week-long route circling the country and travelling out to the islands of Crete and Kastelorizo.
The flame was then “laid to rest” in a ceremony at the Acropolis on Wednesday.
Ahead of Beijing 2008, the Olympic torch traversed the globe in a relay dogged by pro-Tibet, democracy and anti-China protests.
The 2012 relay has taken place with the backdrop of economic turbulence in Greece, which has been left without a government and possibly on the brink of leaving the eurozone by the financial crisis.
Greece has seen huge demonstrations of social unrest in previous months, amid efforts to reach a deal with the European Union on a bail-out for its economy.
A flame was first lit at the modern Olympics at the Amsterdam 1928 summer Games, but it was not until Berlin in 1936 that a torch relay route was set out from Greece to Germany.
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