Two Russians and one American are aboard the rocket, which left Russia's Baikonur Cosmodrome in Kazakhstan at 8.14am local time, the London Telegraph reported.
It is carrying Dan Burbank, from the American space agency Nasa, and Russians Anton Shkaplerov and Anatoly Ivanishin, and is due to arrive at the station on Wednesday.
Once in orbit, the men gave a thumbs-up signal to the on-board cameras and said: "Everything is normal and we are feeling fine", the BBC reported.
The Russian mission is designed to restore faith in Moscow's space program after a string of failures.
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It is the first manned launch since Nasa ended its 30-year shuttle program in July.
The mission also marks the first launch of a Russian Soyuz craft since a similar unmanned rocket carrying cargo crashed into Siberia shortly after launch on August 24.
All manned space travel was suspended for almost three months following the crash, the BBC reported.
Scroll down to see a video of the manned Soyuz launch.