For safety reasons, the torch will not be lit. That may be a relief for Russia as the flame has gone out many times since the torch relay began last month, a minor setback as President Vladimir Putin tries to use the Games to boost Russia's image.
Russian Mikhail Tyurin, American Rick Mastracchio and Japan's Koichi Wakata will have the torch with them on Thursday when they blast off for the International Space Station from the Baikonur cosmodrome, which Moscow rents from Kazakhstan.
Tyurin will hand the torch to fellow cosmonauts Oleg Kotov and Sergei Ryazansky, who are on the orbiting station, when they go on a space walk on Saturday.
The Olympic torch has been carried into space twice before, in 1996 and 2000, but it has never been taken outside a spacecraft.
"Our goal here is to make it look spectacular," Kotov told reporters before his own mission began. "We'd like to showcase our Olympic torch in space. We will try to do it in a beautiful manner. Millions of people will see it live on TV and they will see the station and see how we work."
The torch will be brought back to Earth by Russian Fyodor Yurchikhin, American astronaut Karen Nyberg and European Space Agency astronaut Luca Parmitano on Nov. 11.
It then continues the 65,000-km (40,000-mile) relay which has taken the torch to the North Pole on an atomic-powered ice breaker and will take it to Europe's highest peak, Mount Elbrus, and the depths of Siberia's Lake Baikal.
As well as replacing the gas flame, Russian engineers have equipped the torch with a tether. "It was reworked to take it into open space ... just so that it doesn't fly away," said Sergei Krikalev, head of the Cosmonauts' Training Centre outside Moscow.
While the Russian-made red-and-silver torch is in space, the flame will remain lit on Earth.
The size and grandeur of the relay are in tune with Putin's attempts to use the Games to portray Russia as a modern state and show how far it has come since the collapse of the Soviet Union in 1991.
The former KGB spy has staked a lot of personal political prestige on the two-week Games, which start on Feb. 7 after the torch reaches Sochi.
The Soyuz craft carrying the three-man crew into space on Thursday will be emblazoned with the Sochi 2014 logo and a blue-and-white snowflake pattern. It is due to take off at (10:41 a.m. (0414 GMT) and reach the space station six hours later.
"The Olympics are a huge international event that takes many, many countries cooperating and working together to pull off such a tremendous event," Mastracchio, 53, told a news conference at Baikonur on the Kazakh steppe.
"So in a small way, I think it's great that we bring this symbol up to the international space station, which is another representation of international cooperation."
The arrival of the torch-bearing Soyuz will briefly swell the space station crew to nine, the most that have been on board the orbital outpost since the last U.S. shuttle mission in 2011.
Wakata, 50, will be the first Japanese astronaut to command a crew on the space station.
- President Vladimir Putin