"We have confirmation of the spacecraft separation; Soyuz capsule and crew safely in orbit", NASA TV said online in its blow-by-blow commentary of the take-off.
This will be the first launch of a manned spacecraft after the Soyuz-FG launch vehicle crash on October 11.
It was the first manned launch for the Soviet-era Soyuz since October 11, when a rocket carrying Russia's Aleksey Ovchinin and USA astronaut Nick Hague failed just minutes after blast-off, forcing the pair to make an emergency landing.
Space station veteran and mission commander Oleg Kononenko, 54, Quebec family doctor David Saint-Jacques, 48, and Anne McClain, 39, a USA army helicopter pilot who earned masters degrees from the University of Bath and Bristol in the United Kingdom, are scheduled to blast off at 2:30pm Moscow time from the Baikonur cosmodrome in Kazakhstan.
The Soyuz is the only means of reaching the ISS since the United States retired the space shuttle in 2011.
"Looking forward to having a full crew of six up here again, at least for a few weeks".
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.
"Risk is part of our profession", the 54-year-old said.
NASA astronaut Anne McClain, David Saint-Jacques of the Canadian Space Agency and Oleg Kononenko of Russian space agency Roscosmos were greeted upon arrival Monday by the station's current crew members, who had waited outside the capsule's hatch. "We feel very ready for it", she said.
Roscomos later said the cause of the accident was a defective sensor.
In a successful rehearsal for Monday's flight, a Soyuz cargo vessel took off on November 16 from Baikonur and delivered several tonnes of food, fuel and supplies to the ISS.
Roscosmos, the Russian space agency, is now the only organisation transporting astronauts to the ISS after Nasa ended its space shuttle flights in 2011.
There, they'll meet the European Space Agency's Alexander Gerst, NASA's Serena Auñón-Chancellor and Roscosmos' Sergey Prokopyev, the current crew of the ISS who'll use the Soyuz to return to Earth on December 20.