The torch will be taken by various runners on an international relay that will culminate at the opening ceremony in Rio de Janeiro on 5 August.
The ritual was established 80 years ago for the Berlin Games, based on a ceremony in Ancient Olympia where games were held for more than 1,000 years.
Actor Katerina Lehou, who lit the torch, offered a mock prayer to Apollo, the old Greek god of light and music, at Thursday`s ceremony.
Wearing a long pleated robe, she knelt solemnly to the ground and lit the torch within a few seconds by using a concave mirror to catch the sunlight.
Priestesses and dancers attend the Olympic flame lighting ceremony for the Rio 2016 Olympic Games inside the ancient Olympic Stadium on the site of ancient Olympia (21 April 2016)Image copyrightReuters
She then delivered the flame to Greek world gymnastics champion Eleftherios Petrounias, the first runner in a torch relay that will conclude at the opening ceremony in Rio`s Maracana Stadium.
The chief organiser of the Games, Carlos Nuzman, promised to "deliver history". He said the Olympics would unite Brazil, which is beset by political and economic crises.
"[The torch lighting] brings a message that can and will unite our dear Brazil, a country that is suffering much more than it deserves in its quest for a brighter future," he said in his speech.
Brazil President Dilma Rousseff was forced to cancel her trip to ancient Olympia because of the impeachment threat she faces.
International Olympic Committee (IOC) President Thomas Bach said the flame was "a timeless reminder that we are all part of the same humanity" despite the difficulties that Brazil is facing.
"Rio de Janeiro... will provide a spectacle to showcase the best of the human spirit. In just a few weeks the Brazilian people will enthusiastically welcome the world and amaze us with their joy of life and their passion for sport," he said.
Before the flame arrives in South America it will begin a six-day relay across Greece, passing through the town of Marathon - which gave its name to the long distance race - as well as a camp for refugees and migrants in Athens, the International Olympic Committee has said.
The flame is due to arrive in Brazil on 3 May for a 100-day relay across the country, travelling through 500 cities and villages in every Brazilian state.
It will be carried by about 12,000 torch bearers.
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