An onboard camera showed Japanese astronaut Koichi Wakata pumping the air with his fist as the Soyuz rocket, painted with snowflake patterns, lifted off from the Russian-rented Baikonur launch facility on a crisp, clear morning on the Kazakh steppe.
After a six-hour trip to the station, Russian cosmonaut Mikhail Tyurin crawled through a hatch and handed the unlit torch to his beaming countryman on board, Fyodor Yurchikhin.
"It was great ride and we're happy to be here," said U.S. astronaut Rick Mastracchio, who travelled with Tyurin and Wakata, in a videolink with relatives and space officials 250 miles (400 km) below back on Earth.
Inspired by the Firebird of Russian folklore, the meter-long, red-and-silver torch weighs almost 2 kilograms (4.4 lbs) on Earth, but it floated lazily in zero gravity as Tyurin slowly twirled it in the weightlessness of the orbital outpost.
"It's just an outstanding day and a spectacular launch," William Gerstenmaier, NASA's associate administrator for human exploration and operations, told Reuters at Baikonur.
By tradition, a good-luck charm usually hangs above Soyuz crews when they lift off. Wakata, Tyurin and Mastracchio sat beneath a stuffed polar bear in a blue scarf, a mascot of the first Olympics Russia has hosted since the Soviet era.
The space flight is part of what will be the longest torch relay before a Winter Olympics that President Vladimir Putin hopes will burnish Russia's international image.
"This is a way to show the world what Russia is made of," Dmitry Kozak, the deputy prime minister Putin put in charge of planning the Olympics, said at Baikonur. "We need to put our country, its might and its economic achievements on display."
For safety reasons, the torch will not be lit in what could prove a relief for Russia - the flame has gone out several times since Putin started the relay in Moscow's Red Square on October 6.
On Saturday, cosmonauts Oleg Kotov and Sergei Ryazansky will take the torch outside the station for a space walk. The Olympic torch has gone on voyages aboard spacecraft twice before, in 1996 and 2000, but it has never been taken into open space.
Russian engineers have equipped the torch with a tether to keep it from floating out of the cosmonauts' grip.
As part of its 65,000-km (40,000-mile) relay, the torch has travelled to the North Pole on an atomic-powered ice breaker. It has still to go to the peak of Europe's highest mountain, Mount Elbrus, and the depths of Siberia's Lake Baikal before reaching Sochi on the Black Sea for the start of the Games on February 7.
The trio's arrival at the station, a $100 billion project of 15 nations, briefly swelled its crew to nine - the most on board the outpost since the last U.S. shuttle mission in 2011.
The torch will return to Earth on November 11 with Yurchikhin, European Space Agency astronaut Luca Parmitano and U.S. astronaut Karen Nyberg.