Russia's space agency Roscosmos has now successfully launched five Soyuz rockets since the incident, and does not believe there is a chance of the failure repeating.
American Anne McClain, Canadian David Saint-Jacques and Russian Oleg Kononenko successfully took off from the Baikonur Cosmodrome in Kazakhstan on Monday on their way to the International Space Station.
After launching at 11.31am GMT the three are set to dock at the International Space Station at exactly 5.36pm GMT.
They will start from the same launchpad that Yuri Gagarin did when he became the first man in space in 1961.
The previous launch - involving NASA's Nick Hague and Russia's Aleksey Ovchinin - had to be aborted after the first stage of the rocket failed to separate as planned.
The Soyuz is the only means of reaching the ISS since the USA retired the space shuttle in 2011.
After Monday's successful launch, NASA Administrator Jim Bridenstine tweeted his thanks to his Russian counterpart Dmitry Rogozin and to NASA and Roscosmos space teams "for their dedication to making this launch a success".
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After NASA retired the Space Shuttle in 2011, Russian Soyuz rockets have been the only way to get people to the International Space Station.
"Risk is part of our profession", the 54-year-old said at a press conference.
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 are psychologically and technically prepared for blast-off and any situation which, God forbid, may occur on board".
Saint-Jacques will be the first Canadian resident of the International Space Station since Chris Hadfield, who was on a five-month mission that ended in May 2013. "We feel very ready for it", she said.
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.
Kononenko, McClain and Saint-Jacques smiled and gave thumbs up to the cheering crowd including relatives as they ascended into the Soyuz capsule on Monday morning.
A Russian investigation attributed the failure to a sensor that was damaged during the rocket's final assembly.