The Soyuz MS-11 spacecraft lifts off on Monday.
The crew who set off on Monday will spend six-and-a-half months on board the station.
The accident in October was the first aborted crew launch for the Russian space program since 1983, when two Soviet cosmonauts safely jettisoned after a launch pad explosion.
A Soyuz-FG rocket carrying NASA astronaut Nick Hague and Roscosmos' Alexei Ovchinin failed two minutes into its flight on October 11, activating an automatic rescue system that sent their capsule into a steep ride back to Earth.
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.
NASA's Anne McClain, the Canadian Space Agency's David Saint-Jacques and Russian cosmonaut Oleg Kononenko reached orbit minutes after the smooth launch from Baikonur Cosmodrome in Kazakhstan at 3:31 a.m. PT.
"We are psychologically and technically prepared for blastoff and any situation which, God forbid, may occur on board", said Kononenko, the 54-year-old crew commander, according to Radio Free Europe.
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.
RFE also quoted McClain, 39, saying: "We feel very ready for it".
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.
A rehearsal unmanned flight, which delivered cargo including food and fuel supplies, was successfully carried out in mid-November. The three Expedition 57 members are expected to stay in space for 194 days.
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.
The station's current crew of NASA's Serena Aunon-Chancellor, Russian Sergei Prokopyev and German Alexander Gerst were waiting to greet the newcomers.