Commander Alexander Misurkin of Roscosmos and flight engineers Mark Vande Hei and Joe Acaba of NASA lifted off from the Baikonur Cosmodrome at 3:17 a.m. local time on Wednesday (2117 GMT/1717 EDT on Tuesday).
The crew is set for a fast-track transit to the station, which orbits about 250 miles (400 km) above Earth, to begin a five-month mission.
They are due to arrive at the Space Station by mid-morning on Wednesday but should the fast-track approach fails, the Soyuz will take two days to reach the ISS.
Misurkin, Vande Hei and Acaba will join NASA astronaut Randy Bresnik, Russia's Sergey Ryazanskiy and Paolo Nespoli of the European Space agency who have been aboard the orbital outpost since July.
To commemorate the upcoming 60th anniversary on Oct.4 of the launch of the first artificial satellite, Sputnik 1, the Soyuz crew are using its small model as a zero gravity indicator.