The run-up to the Feb. 9-25 Olympics has been overshadowed by the escalating crisis on the Korean peninsula triggered by North Korea's nuclear and ballistic missile tests but organisers said the Games would be safe.
The traditional ceremony, introduced for the first time ahead of the 1936 Berlin Olympics, did not benefit this time from the Greek sun.
Light rain and clouds forced the high priestess, played by actress Katerina Lechou, to deploy Monday's backup flame instead of the reflector used to light the flame with the sun's rays.
"Our dream of hosting the Olympic winter Games has now become a reality. Korea is only the second Asian nation to have the honour of hosting the winter Games," Games chief Lee Hee-beom said.
"We want the international community to understand that we are committed to hosting a safe and secure Olympic winter Games."
The ceremony inside the stadium, site of the ancient Olympics, was also attended by South Korean Prime Minister Lee Nak-yeon, International Olympic Committee President Thomas Bach and the President of Greece, Prokopis Pavlopoulos.
"The Olympic Games are sacred and universal," Bach said.
"They stand above and beyond all the differences that divide us. In our fragile world that seems to be drifting apart, the Olympic Games have the power to unite humanity in all its diversity."
Former Manchester United midfielder Park Ji-sung, among the most successful and decorated athletes from his country, was the first South Korean to run with the torch, picking up the flame from Greece's Nordic skier Apostolos Aggelis, the first torch-bearer, just outside the ancient stadium.
"We will make sure to show the world how we have grown up, how we can organise this sports event," Park told reporters after his short run.
"This is bigger than Seoul (summer Olympics) 1988. These are the largest winter Olympics ever and I am excited to be part of it."
The flame is due to arrive in South Korea on Nov. 1 for the start of the domestic torch relay as organisers look to boost local enthusiasm amid low ticket sales.
Tensions on the Korean peninsula have risen in recent months as Kim Jong Un and U.S. President Donald Trump exchanged threats and insults over the North's nuclear and missile development programme.
(Reporting by Karolos Grohmann, editing by Ed Osmond)
