The ceremony was held with actresses dressed as ancient priestesses at the birthplace of the Greek games held in antiquity, with the flame lighting using a parabolic mirror.
Actress Ino Menegaki, in the role of high priestess, called out to the ancient god of the sun, Apollo, before the flame was lit and passed to 18-year-old Greek alpine skier Ioannis Antoniou. NHL star Alex Ovechkin was the first Russian involved in the torch relay.
Moments before the being handed the torch, the Washington Capitals winger said: "To be honest with you, it's going to be (an) experience for all my life, and you know, I am proud to be Russian and proud to be here."
Newly elected International Olympic Committee President Thomas Bach was present at the ceremony. He said he had discussed an ongoing controversy with games organizers about Russia's record on the treatment of gays and had received assurances of non-discrimination at the games.
"We have the assurances of the highest authorities in Russia, and yesterday I spoke with the Russian delegation here in Olympia again and they reassured us that the Olympic Charter will fully apply for all the participants of the games," Bach said.
Sunday's 20-minute ancient re-enactment, involving 21 priestesses dressed in cream-colored pleated dresses, marked the start of the build-up to the games — centred on the torch relay.
The Russian leg of the relay is set to cover more than 40,000 miles before the Winter Games, carrying the torch by hot-air balloon, dog sled and a nuclear-powered ice breaker before its scheduled trip to space on Nov. 7.
"The Olympic Games ... should inspire the people of the world and especially the political authorities by showing them that quarrels and conflicts can be addressed with peaceful means," Bach said before the ceremony. "I think it will have a very positive effect on Russia. It will show a new Russia to the world and also open up civil society."
Sochi organizers promised the torch route would be within an hour's travel of an estimated 90 per cent of Russia's population
"There is no greater privilege than to stand here in the spiritual home of the Olympic Movement," Dmitry Chernyshenko, chief organizer of Sochi 2014, said at Ancient Olympia. "This is the beginning of an epic journey for the Olympic Torch, a journey that will change Russia forever."
The weekend ceremony was overshadowed by the arrest in Athens of the leadership of the country's far-right Golden Dawn party on charges of forming a criminal organization.
The Greek leg of the relay will cover around 1,250 miles until an Oct. 7 handover ceremony in the Panathenian Stadium in Athens, venue of the first modern Olympics in 1896.
Some 2,800 athletes from more than 80 countries are due to compete at Sochi.