The Soyuz MS-11 docked to the ISS in the automatic mode at 22:38 Moscow time after a six-hour orbital flight.
The three will spend the next six months onboard the International Space Station.
For a while, the arrival of the three new crewmembers returned the ISS crew complement to a total of six.
They escaped unharmed but the failed launch was the first such incident in Russia's post-Soviet history and a new setback for the country's once proud space industry.
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The three current inhabitants - Alexander Gerst of Germany, Serena Auñón-Chancellor of the United States and Sergey Prokopyev of Russian Federation - plan to return December 20 aboard a Soyuz module that has been docked to the station since June. Auñón-Chancellor, Gerst and Prokopyev are scheduled to remain aboard the station until December 20.
The latest trip comes less than two months after a previous mission on October 11 failed, when two astronauts from the United States and Russian Federation were forced to make an emergency landing, as a result of a problem with the booster. They managed to emerge safely despite the harrowing ordeal.
That same month they will be joined by another three spacefarers, a crew which will comprise the two men that aborted the launch in October, Nick Hague (NASA) and Alexey Ovchinin (Roscosmos) and a newcomer, Christina Koch (NASA).
A Russian investigation attributed the failure to a sensor that was damaged during the rocket's final assembly.
Russian space officials took measures to prevent the repeat of such a rocket failure. 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".
This is the first launch of a manned spacecraft after the abortive blastoff of the Soyuz carrier rocket on October 11. That means they will be coordinating the launch of the SpaceX Crew Dragon capsule on January 7 and that of the Boeing Starliner in March.