Russian Soyuz Commander Alexander Samokutyayev, NASA Flight Engineer Ron Garan and cosmonaut Andrey Borisenko are to join three other crew members aboard the orbital station after a two-day trip from Earth aboard the cramped spacecraft, an upgraded model of a Soviet-designed standby.
Russian Mission Control said the three men lifted off on schedule from the Baikonur cosmodrome at 0418 local time (2218 GMT on Monday).
"The Soyuz-TMA 21 spacecraft has reached orbit," Samokutyayev, strapped in with his two crewmates, reported to Russian Mission Control a few minutes into the flight after the rocket stages dropped off.
The crew in white space suits flashed thumbs up to onboard cameras and a stuffed toy mascot began floating above their heads as they entered weightlessness.
Once it was safely in orbit, applause broke out at the cavernous Mission Control center in a northern Moscow suburb, named after Gagarin's mentor, the legendary chief designer of the Soviet space programme Sergei Korolyov.
It is the first flight for Russians Samokutyayev and Borisenko, while Garan has logged 13 days in space during a 2008 shuttle mission.
The launch comes less than a week before the 50th anniversary of Yuri Gagarin's historic flight from the same, once-secret Baikonur launch facility to become the first human in orbit.
Tuesday's successful launch of the Soyuz -- which was named after Gagarin and his portrait daubed across its hull -- will likely assuage concerns over reliance on the single-use Russian spacecraft as NASA mothballs its shuttle fleet later this year.
Lift off had been postponed from March 30 due to a glitch in the upgraded Soyuz's communication system.
Garan, an avid twitter user and blogger, has promised to keep up the information flow from orbit. On Sunday, he tweeted pictures of himself getting a last haircut on Earth and called Gagarin's flight "a giant leap in our evolution as a species."
He and his crewmates will spend six months aboard the station, a $100 billion project of 16 nations that has been under construction about 220 miles above Earth since 1998.
The growing orbital complex, a mix of mostly Russian and American-built modules, can now accommodate a six-member crew at all times.
Russian cosmonaut Dmitry Kondratyev, U.S. astronaut Cady Coleman and European Space Agency's Paolo Nespoli of Italy have been aboard the station since mid-December.
(Editing by Philippa Fletcher)