"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.
It is the first manned space mission since the October drama, which ended in an emergency landing after a failure mid-flight.
The trio blasted off aboard a Russian Soyuz rocket two months after a similar rocket launched from the same site malfunctioned, forcing astronauts Aleksey Ovchinin and Nick Hague to make an emergency re-entry.
Russian cosmonaut Oleg Kononenko, Anne McClain of NASA and David Saint-Jacques of the Canadian Space Agency launched for a six-and-a-half month mission on the International Space Station at the expected time of 1131 GMT.
Russia's state space corporation, Roscosmos, traced the failure to a damaged sensor and found that two other Soyuz rockets might have the same defect.
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.
At a press conference on the eve of the launch, crew commander Kononenko said the astronauts "absolutely" trusted teams preparing for the flight.
McClain, a 39-year-old former military pilot, said the crew looked forward to going up.
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 rehearsal unmanned flight, which delivered cargo including food and fuel supplies, was successfully carried out in mid-November.
"We are psychologically and technically prepared for blast-off and any situation which, God forbid, may occur on board".
Roscosmos, the Russian space agency, is now the only organisation transporting astronauts to the ISS after Nasa ended its space shuttle flights in 2011.
Kononenko, McClain and Saint-Jacques will officially become the Expedition 58 crew when Gerst, Aunon-Chancellor and Prokopyev depart the station for home on December 20.
Russian Federation said last month the October launch had failed because of a sensor damaged during assembly at the Baikonur cosmodrome, but insisted the spacecraft remained reliable.