As rain fell actors in ancient Greek costume resorted to the backup flame at the ruins of the 2,600-year-old Temple of Hera instead of a scheduled ceremony using a parabolic mirror to kindle the flame.
The torch relay will take it around Greece and on to 2018 hosts South Korea.
Dignitaries at the ceremony included Greek President Prokopios Pavlopoulos, South Korean Prime Minister Lee Nak-Yon and International Olympic Committee President Thomas Bach.
"Then and now, the Olympics is a symbol of hope and peace. We are carrying the ancient traditions to the future. The Games are universal and stand above all differences that divide us and are here to unite humanity," Bach said. "Our Olympic values have stood the test of time of peace and understanding."
President of the Pyeongchang 2018 Organising Committee Lee Hee Beom said the Winter Games in his country will be "safe and secure".
The South Korea government has promised that the Pyeongchang Games would be safe after some nations suggested they may skip the event if tensions over North Korea's nuclear ambitions worsen.
The Pyeongchang Winter Games will be held from February 9-25 only 80km from the heavily guarded border with the nuclear-armed North.
The South has successfully staged several international sporting events including the 2002 FIFA World Cup despite decades of military tensions on the peninsula.
he torch relay will cover 2,129 kilometres on Greek territory and will arrive at the Acropolis in Athens on October 30. Participating will be 505 torchbearers and 36 welcome ceremonies will be held in 20 districts during the eight days.
The torch harks back to the ancient Olympics, when a sacred flame burned throughout the Games. The tradition was revived in 1936 for the Berlin Olympics.