Nasa astronaut Anne McClain, David Saint-Jacques of the Canadian Space Agency and Oleg Kononenko of the Russian space agency Roscosmos have begun their six-hour trip to the orbital laboratory.
They lifted off as scheduled on Monday from the Russian-leased Baikonur cosmodrome in Kazakhstan.
A Soyuz-FG rocket carrying Nasa astronaut Nick Hague and Roscosmos’ Alexei Ovchinin failed two minutes into its flight on October 11.
They were to dock at the orbiting outpost six hours later - but the booster suffered a failure minutes after the launch.
The astronauts activated an automatic rescue system which sent their capsule into a steep ride back to Earth.
Video shows moment of malfunction
A Russian investigation attributed the failure to a sensor that was damaged during the rocket’s final assembly.
Since the mishap, four successful Soyuz launches have been conducted to clear the path for the crew’s launch.