SpaceX launched the replacements as soon as possible at NASA's request, sending the US, French and Russian astronauts on an expected eight- to nine-month mission.
The four launched on Friday and should arrive at the orbiting lab the next day, filling the vacancies left by their evacuated colleagues in January and bringing the space station back to full staff.
NASA had to put spacewalks on hold and deferred other duties while awaiting the arrival of NASA's Jessica Meir and Jack Hathaway, France's Sophie Adenot and Russia's Andrei Fedyaev.
They will join three other astronauts - one American and two Russians - who kept the space station running the past month.
Satisfied with medical procedures already in place, NASA ordered no extra check-ups for the crew before lift-off and no new diagnostic equipment was packed.
An ultrasound machine already up there for research went into overdrive on January 7 when used on the ailing crew member.
NASA has not revealed the ill astronaut's identity or health issue.
All four returning astronauts went straight to the hospital after splashing down in the Pacific off California.
It was the first time in 65 years of human spaceflight that NASA cut short a mission for medical reasons.
In preparation for moon and Mars trips where health care will be even more challenging, the new arrivals will test a filter designed to turn drinking water into emergency IV fluid, try out an ultrasound system that relies on artificial intelligence and augmented reality instead of experts on the ground, and perform ultrasound scans on their jugular veins in a blood clot study.
They also will demonstrate their moon-landing skills in a simulated test.
Adenot is only the second French woman to launch to space.
She was 14 when Claudie Haignere flew to Russia's space station Mir in 1996, inspiring her to become an astronaut.
Haignere travelled to Cape Canaveral to cheer her on.
Hathaway, like Adenot, is new to space, while Meir and Fedyaev are making their second station trip.
On her first mission in 2019, Meir took part in the first all-female spacewalk.
The other half of that spacewalk, Christina Koch, is among the four Artemis II astronauts waiting to fly around the moon as early as March.
SpaceX launched the latest crew from Cape Canaveral Space Force Station.
Elon Musk's company is preparing its neighbouring Kennedy Space Center launch pad for the super-sized Starships, which NASA needs to land astronauts on the moon.
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