American Tom Marshburn, Russian Roman Romanenko and Canadian Chris Hadfield traveled two days in the capsule before linking up with the space station's Russian Rassvet research module.
The docking took place around 255 miles (410 kilometers) above the capital of Kazakhstan.
Almost three hours passed before pressure was equalized between the capsule and the space station, allowing for safe entrance.
As the hatches were unlocked, the arriving trio was welcomed by NASA astronaut Kevin Ford and Russian colleagues Oleg Novitsky and Yevgeny Tarelkin.
The six colleagues exchanged hugs and posed for photos as they floated in the weightless atmosphere of the station.
Minutes after entry, Hadfield could be heard saying in English: "I love what you've done with the place."
Hadfield flew to the space station in 2001, when he spent 11 days at the facility and performed two spacewalks. He will take over as the space station's first ever Canadian commander in its fourteen year history when the crew now onboard prepares to leave in March.
Family members spoke for the first since the launch with the astronauts in a linkup from the Korolyov space center outside Moscow.
"It was just a heck of a ride for the three of us. It's like being on a crazy dragster, just a fun, crazy zip up to space," Hadfield said, speaking to his son.
The incoming crew will spend nearly five months at the space station before returning to earth.
Their mission began with a launch from the Russian-leased Baikonur space port in southern Kazakhstan.
The International Space Station is the biggest orbiting outpost ever built and can sometimes be seen from the Earth with the naked eye. It consists of more than a dozen modules built by the U.S., Russia, Canada, Japan and the European Space Agency.
The astronauts will conduct some 50 scientific experiments including a test for a system aimed at predicting natural calamities.
