It launched from Russia's manned-space facility in the frigid steppes of Kazakhstan at 6:12 p.m. (1212 GMT). It separated from its final rocket stage and went into orbit about 15 minutes later.
American Tom Marshburn, Russian Roman Romanenko and Canadian Chris Hadfield will travel for two days in the capsule, before docking with the space station where three other astronauts are already on board.
The docking coming close to Christmas added to the high emotional valence of spaceflight for Hadfield.
"There are certain times of the year and certain times in life that are special by everybody's traditions. In my family's tradition, this is maybe the most special time of the year," he said.
Around four hours before the launch, the astronauts posed for photos, ran final suit checks and chatted with relatives through protective glass designed to protect them from infection.
Romanenko was seen off by his father Yuri, who set a record for time spent in space during a mission in the 1970s.
"My dad carried out a spaceflight in a two-person crew ... on a similarly cold day 35 years ago and that was one of the first long-term flights," Romanenko said at a news conference on the eve of the launch.
Typically, the crew performs a final outdoor salute to top space officials before mounting the bus taking them to the Soyuz, but the practice was forgone on this occasion because of the severe cold; the temperature at launch time was -17 C (2 F).
Before the astronauts were tightly packed into the cramped capsule, they exchanged greetings with Russian Federal Space Agency chief Vladimir Popovkin.
Although space travel has long fascinated the general public, interest has flagged in recent decades as tightened budgets have constrained ambitions.
Hadfield displayed optimism about the future of the industry and said that the voyages to the moon, which last happened 40 years ago, set an important precedent.
"What we are doing today as a group is continuing through that door and learning the things we need to do and taking one small step at a time so that we can better understand where we are in the universe," he said.
(Copyright 2012 by The Associated Press. All Rights Reserved.)