This is the first manned Russian rocket launch since a dramatic Soyuz failure on October 11.
The mission marked the 100th orbital launch of 2018, and the first time in 28 years that humanity reached that number of launches within a calendar year. A Russian investigation attributed the failure to a sensor that was damaged during the rocket's final assembly.
Russian cosmonaut Oleg Kononenko, Anne McClain of NASA and David Saint-Jacques of the Canadian Space Agency blasted off for a six-and-a-half month mission on the International Space Station (ISS) on schedule today at 11.30am GMT.
Speaking before the trip on Sunday, crew commander Oleg Kononenko affirmed his crew "absolutely" trusted the flight's preparation.
The Soyuz was "successfully launched into orbit", Roscosmos wrote on Twitter.
Soyuz heads to ISS on first manned mission since October failure
"We are psychologically and technically prepared for blast-off and any situation which, God forbid, may occur on board", the 54-year-old said.
Kononenko, McClain and Saint-Jacques were all smiles as footage broadcast by NASA TV showed them preparing to enter the Soyuz capsule before launch.
Roscosmos, the Russian space agency, is now the only organisation transporting astronauts to the ISS after Nasa ended its space shuttle flights in 2011.
In a successful rehearsal for today's flight, a Soyuz cargo vessel took off on 16 November from Baikonur and delivered several tonnes of food, fuel and supplies to the ISS.
After the Soyuz docks with the space station, the mission is expected to last 194 days, according to TASS, which means the trio will remain on board through July 2019.
The Russian rocket carries USA astronaut Anne McClain, Russian cosmonaut Oleg Kononenko? and CSA astronaut David Saint Jacques.
The Expedition 58 astronauts will briefly join NASA astronaut Serena Auñón-Chancellor, Alexander Gerst of the European Space Agency and cosmonaut Sergey Prokopyev, who are scheduled to leave the space station on December 20.
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