First-time astronauts Kathleen Rubins of NASA and Takuya Onishi of the Japanese space agency set off for a four-month mission at the ISS with two-time Russian cosmonaut Anatoly Ivanishin at 0136 GMT.
"And lift-off!" said a commentator on NASA TV, which broadcast footage of the launch in Kazakhstan.
The trio's launch was delayed by over two weeks as Russian space officials carried out further software tests on the modified vehicle.
Features of the new Soyuz series include upgraded boosters, an improved navigation system, strengthened shielding from debris and more cells on the craft's solar panels.
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The molecular biologist, accepted into the space program in 2009, will also become the first person to sequence DNA in space during her mission.
Takuya Onishi, who trained as a pilot on Japan's largest commercial airliner is the eleventh Japanese national to enter space.
His journey to the ISS where he will participate in experiments connected to the Japanese space agency's Kibo program coincides with the Tanabata star festival celebrated across his homeland.
The ISS space laboratory has been orbiting Earth at about 28,000 kilometres per hour since 1998.