Gymnast Lefteris Petrounias, the 2015 rings world champion, was the first torchbearer.
He became the first from his sport to carry the flame in the Ancient Stadium.
He is the first runner in a Relay that will ultimately involve almost 13,000 people in a journey that will end at the Opening Ceremony in Rio de Janeiro on August 5.
Petrounias took the flame to pay a brief homage at the Coubertin grove, where the first runner traditionally visits the monument to Olympic founder Baron Pierre de Coubertin.
"Today is one of the rare moments when the past and future of humanity connects," said International Olympic Committee President Thomas Bach.
"These Olympic Games will send a message of hope in troubled times and the flame will carry this message to all corners of Brazil and indeed the world.
"May today's lighting of the Olympic flame be another reminder to everyone to uphold the spirit of the Olympic Games and to build a better world through sport.
Bach also appeared to make reference to Brazilian President Dilma Rousseff, who is facing impeachment proceedings amid a corruption scandal in the country.
She had originally planned to attend the event here.
"Despite the difficulties that Brazil is facing today, the flame is a timeless reminder that we are all part of the same humanity," Bach said.
The first Brazilian to carry the flame was volleyball player Giovane Gavio, who also did so when it visited Rio de Janeiro in 2004.
Later that year he was a member of the gold medal winning team in Athens.
“I did not know whether to laugh or cry," he told insidethegames.
"I think this is even more exciting because there is such a lot of history here, so many champions have passed through here.
"I love Greece, my wife’s family are from Greece and the last time I came here, I won an Olympic gold medal."
His fellow volleyball player Carlos Nuzman carried the flame along the same stretch of ground in the London 2012 Relay.
Here he witnessed the ceremony as President of Rio 2016.
"We in Brazil understand our responsibility as guardians of this Olympic flame," he said.
"Maybe more than ever, the guiding values of Olympism represent a source of hope.
"The journey of the flame will energise our young people, unite our communities and showcase the timeless power of the Games to create a better world.
"We believe Rio 2016 will excite and unite the world."
The ceremony began in the sacred altis of the goddess Hera.
A simple drum announced the arrival of the priestesses, clad in pale turquoise.
With them was a herald dressed in olive green with a conch horn.
In the days of antiquity, heralds would announce that the Games were coming.
Priestess Katerina Lehou stepped forward to offer a prayer to Apollo.
"Apollo god of the sun and the idea of light, send your rays and light the torch for the hospitable city of Rio," she said.
Then she dipped a specially fashioned silver torch into a reflective bowl to light the flame.
This was placed in an ancient pot or amphora, to be carried by another priestess, known as the Estiada.
The procession of the flame party to the ancient stadium was accompanied not as in previous years by a boy but by four young girls dressed in similar costumes to the priestesses.
Choreographer Artemis Ignatiou told insidethegames: ’’We wanted to do something a little different this year."
In the Stadium, the young men known as Kouroi danced as if they were statues come to life.
On the hillside, the Priestesses represented the Goddesses of the Sea.
In the words of ancient artists they were "beautiful young maidens controlling the winds and rough seas and dancing with the dolphins".
As the performance came to a close, the men and women danced together in a circle on the hillside, a vision of olive and turquoise, the symbolic colours of this ceremony.
The costumes had been designed to display the colours and to highlight the movements of the dance.
They were the work of Eleni Kyriacou, now a designer in Athens but once a pupil of Alexander McQueen in London.
‘’I wanted to intensify the sense of rhythm, especially during the dance movement,’’ said Kyriacou.
The soundtrack was composed by Yiannis Psimadas and featured the ancient Greek lyre.
He had travelled to the Ancient Stadium to seek inspiration for his composition.
“My music is borne from the light of Olympia," he said.
"The challenge is to tell the complete story in a very short piece."
As the flame reached the village, it was carried, appropriately, by Kostas Georgiadis, Dean of the International Olympic Academy (IOA).
Since 1961, the IOA has been an essential part of life in Olympia.
This year, 20 postgraduate students on the international masters programme also ran with the flame.
“This is one of the highlights of their time with us and it gave them an opportunity to feel these values of Olympism," said Georgiadis.
The flame headed away towards the ancient settlement of Elis, home of Coroebus, the first Olympic champion in 776 BC, before heading across the water.
The journey through Greece is from Z to A.
On the first night the flame rests in Zakynthos and the final destination is Athens in a week’s time after a journey of some 2,235 kilometres across Greece.