The SpaceX Dragon Endeavour spacecraft arrived at the orbiting station at 0640 GMT on Friday, the US space agency said in a statement.
NASA's Stephen Bowen and Warren Hoburg, Russia's Andrey Fedyaev and Sultan al-Neyadi of the United Arab Emirates entered the station about two hours later, the livestream showed.
A SpaceX Falcon 9 rocket carrying the spacecraft had blasted off to the station on Thursday after the launch was scrubbed just minutes before liftoff earlier in the week.
The crew will spend six months on the station, where they will conduct more than 200 science experiments and technology demonstrations, according to SpaceX.
The mission was the first space flight for Neyadi, Hoburg and Fedyaev.
Neyadi, 41, is the fourth astronaut from an Arab country and the second from the oil-rich UAE to journey to space.
Fedyaev is the second Russian cosmonaut to fly to the ISS aboard a SpaceX rocket. NASA astronauts fly regularly to the station on Russian Soyuz craft.
Space has remained a rare venue of cooperation between Moscow and Washington since the Russian offensive in Ukraine placed them in sharp opposition.
More about: SpaceX
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