The spacecraft blasted off on schedule from Russia's Baikonur cosmodrome in the barren Kazakh steppe at 2102 GMT, carrying cosmonaut Oleg Kononenko, US astronaut Kjell Lindgren and Kimiya Yui of Japan.
As the Soyuz TMA 17M rocket surged skywards from the launch pad, the fire from the boosters set the inky night sky aglow.
Russian officials breathed a sigh of relief, with the space agency Roscosmos saying in a statement that the third stage of the Soyuz rocket separated on time and the crew were "feeling well."
All eyes were trained on the launch after Russia was in May forced to delay the astronauts' departure because a supply ship had crashed back to Earth following a rocket failure.
The three astronauts were originally scheduled to travel to the orbiting lab in late May but Russia put all space travel on hold after the failure of the unmanned Progress freighter taking cargo to the ISS in late April.
The doomed ship lost contact with Earth and burned up in the atmosphere. The failure, which Russia has blamed on a problem in a Soyuz rocket, also forced a group of astronauts to spend an extra month aboard the ISS.
"Training...Check. Equipment...Check. Rocket...Check. Press conference...Check. We are ready to fly!!" 42-year-old Lindgren said on Twitter before the liftoff.
The team said they had faith in the Russian space programme, adding that the delay had given them extra time to prepare for their 163-day space mission.
The trio said they were Star Wars fans and had chosen the R2-D2 robot, a key character in the film series, as a zero-gravity indicator for their mission.
Once the toy - which Lindgren said he had chosen with the help of his children - begins to float, the crew will know they have reached orbit.
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