The launch of the rocket will be observed by the head of Roscosmos, Dmitry Rogozin, the head of NASA's manned flights department, William Gerstenmayer, and the governor-general of Canada, Julie Peyette (former astronaut of the Canadian Space Agency).
Aboard the International Space Station, he will conduct a number of science experiments, with some focusing on the physical effects of the weak gravity astronauts experience in orbit as well as how to provide remote medical care.
NASA's Anne McClain, Russia's Oleg Kononenko, and Canadian Space Agency astronaut David Saint-Jacques - reached orbit about 10 minutes after taking off from Kazakhstan on the Soyuz MS-11 rocket.
If all goes as planned, six hours later they will dock with the space station.
McClain, Saint-Jacques and Kononenko will live on the ISS for six-and-a-half months.
Now that crewed flights have resumed, Gerst and two other crew members, NASA's Serena Auñón-Chancellor and Russia's Sergey Prokopyev, are due to head back to Earth on December 19.
The astronauts are slated to stay on the ISS until July 2019.
Speaking before the trip on Sunday, crew commander Oleg Kononenko affirmed his crew "absolutely" trusted the flight's preparation.
RFE also quoted McClain, 39, saying: "We feel very ready for it".
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.
Less than two minutes into that flight, one of the rocket's four external boosters failed to separate and accidentally struck the core stage of the rocket, sending it spinning out of control.
Russia's space agency Roscosmos has successfully launched a manned Soyuz rocket carrying astronauts to the International Space Station for the first time since October's aborted mission. The pair landed safely about 12 miles east of the city of Dzhezkazgan in Kazakhstan.
Afterward, investigators said they believed other Soyuz models may have been defective, but said additional checks had been introduced.