This will be the first launch of a manned spacecraft after the Soyuz-FG launch vehicle crash on October 11.
The launch was closely scrutinised because of the abortive mission to the ISS on October 11, which ended two minutes after take-off when a rocket failure forced its two-man crew to perform an emergency landing.
October's accident had highlighted the "smart design of the Soyuz and the incredible work that the search and rescue people here on the ground are ready to do every launch", he said.
Russian Federation said last month the launch of the Soyuz rocket failed because of a sensor that was damaged during assembly at the Baikonur cosmodrome, but officials insisted the spacecraft remains reliable.
It will be the fourth visit to the ISS for Russian cosmonaut Mr Kononenko, while the trip will be the first for both Anne McClain from the USA and David Saint-Jacques of the Canadian Space Agency.
"Risk is part of our profession", crew commander Oleg Kononenko told a news conference at Baikonur, adding they "absolutely" trusted teams preparing them for the flight.
McClain, Saint-Jacques and Kononenko will spend more than six months doing research and experiments in biology, Earth science, physical sciences and technology.
"We are psychologically and technically prepared for blast-off and any situation which, God forbid, may occur on board".
The Soyuz was "successfully launched into orbit", Roscosmos wrote on Twitter.
Canadian astronaut David Saint-Jacques blasted off from Kazakhstan this morning aboard a Russian Soyuz rocket bound for the International Space Station.
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.
Afterward, investigators said they believed other Soyuz models may have been defective, but said additional checks had been introduced.
NASA's Anne McClain, Russia's Oleg Kononenko, Canadian Space Agency's David Saint-Jacques.
The ISS space laboratory has been orbiting the Earth at roughly 28,000 kilometres per hour since 1998.
On the space station, the crew of NASA's Serena Aunon-Chancellor, Russian Sergei Prokopyev and German Alexander Gerst were waiting for their arrival.