It is the first attempt to send astronauts to space after a mission in October that saw two crew members only narrowly escape after being forced to make an emergency landing just minutes after take-off.
The hatch of the capsule carrying NASA astronaut Anne McClain, David Saint-Jacques of the Canadian Space Agency and Oleg Kononenko of Russian space agency Roscosmos was opened while the station was flying over the southern coast of Yemen.
They'll spend about six hours in orbit before docking at the ISS around 12:30 p.m, the National Aeronautics and Space Administration said.
They will start from the same launchpad that Yuri Gagarin did when he became the first man in space in 1961.
The launch comes after a Soyuz rocket carrying Russia's Aleksey Ovchinin and USA astronaut Nick Hague failed on October 11 just minutes after blast-off, forcing the pair to make an emergency landing. They should reach the International Space Station by noon.
Astronauts from Russian Federation, the USA and Canada left from Kazakhstan on a mission bound for the International Space Station at 17:30 (11:30 GMT).
Roscosmos, the Russian space agency, is now the only organisation transporting astronauts to the ISS after Nasa ended its space shuttle flights in 2011.
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While flight commander Kononenko is beginning his fourth mission to add to an impressive 533 days in space, both Saint-Jacques and McClain are making their maiden trip.
"We are psychologically and technically prepared for blastoff and any situation which, God forbid, may occur on board", the 54-year-old said.
There, they'll meet the European Space Agency's Alexander Gerst, NASA's Serena Auñón-Chancellor and Roscosmos' Sergey Prokopyev, the current crew of the ISS who'll use the Soyuz to return to Earth on December 20.
RFE also quoted McClain, 39, saying: "We feel very ready for it".
A few minutes after the rocket lifted off the Russian space agency Roscomos announced that the capsule was "successfully launched into orbit".
The accident highlighted the "smart design of the Soyuz and the incredible work that the search and rescue people here on the ground are ready to do every launch", he said.
New astronauts Anne McClain of the United States and David Saint-Jacques of Canada, together with veteran cosmonaut Oleg Kononenko of Russian Federation, are due to arrive at the space station after a trip of six hours.
A Russian investigation attributed the failure to a sensor that was damaged during the rocket's final assembly.