The torch for the London Games will set off on a seven-day journey across Greece before it leaves for Britain on May 18.
"We promise to protect the Flame; to cherish its traditions and to stage an uplifting torch relay of which we can all be proud and which can inspire a generation," Mr Coe said.
"As torchbearers lift the Olympic flame in the days and months ahead, it is our hope that they will also lift the spirits and hopes of people across Britain and across world."
Actress Ino Menegaki, playing the role of a high priestess, lit the torch at the site of the ancient Olympics in the western Peloponnese.
London is the only city to have lit the torch twice in Olympia.
The 70-day torch relay will travel 12,800 km around Britain, taking in 1,018 villages and the 1,085-metre summit of Snowdon, before culminating with the lighting of the Olympic cauldron in the Olympic Stadium on the opening day of the Games on July 27.
The relay will also take in landmarks around Britain with the flame travelling by canal boat, cable car, tram, steam train, hot air balloon and even motorcycle sidecar on the Isle of Man TT course.
More than 95 per cent of the population will be within an hour of the route.