American Michael Hopkins and Russians Oleg Kotov and Sergei Ryazansky travelled six hours in the capsule from the Russian-leased launch pad in Kazakhstan before linking up with the space station's Russian Poisk research module at 6.45 am Moscow time.
Kotov is the most experienced member of the crew with two previous six-month missions in space under his belt, while Hopkins and Ryazansky are both on their first missions.
Kotov and Ryazansky will have the honor of taking the Olympic torch into open space in November as part of the relay of the Olympic flame ahead of the Winter Games being held in Russia's Sochi in February. The torch will not be lit however, because of safety concerns. It will only arrive at the station in November with the next mission.
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Radiant but visibly tired, the astronauts were yawning as they were talking to their families. They had been up for about 20 hours.
Hopkins' mother described the launch as a "heart-stopping experience."
"It was a pretty good ride, mom. It was a lot of fun," Hopkins replied in the live broadcast on NASA TV.