Chris Cassidy of the United States and Russians Pavel Vinogradov and Alexander Misurkin traveled six hours in the capsule before linking up with the space station's Russian Rassvet research module over the Pacific Ocean, just off Peru, at 02:28 GMT.
"It's such a beautiful sight, hard to believe my eyes," the 59-year-old Vinogradov, who had been in space in 1997 and 2006, was heard saying on NASA TV.
The incoming crew will spend five months in space before returning to Earth.
About two hours passed before pressure equalized between the capsule and the station, allowing safe entrance.
"Hey, is anyone home?" joked Vinogradov as he floated into the station.
Cassidy, Vinogradov and Misurkin were greeted with cheers and hugs by American Tom Marshburn, Russian Roman Romanenko and Canadian Chris Hadfield, who have been at the station since December.
The astronauts then had a brief session with Mission Control outside Moscow, talking with friends and relatives.
"You're such a star! I'm really proud of you!" Misurkin's tearful mother said. The 35-year-old Russian is on his first flight into space.
Their mission began with a late-night launch from the Russian-leased Baikonur launch pad in Kazakhstan.
It was the first time a space crew has taken such a direct route to the orbiting lab.
The new maneuver was tested successfully by three Russian Progress cargo ships, unmanned versions of the Soyuz used to ferry supplies to the space station. Russian cosmonauts have described the two-day approach maneuver in the cramped Soyuz as one of the most grueling parts of missions.
Vinogradov said at a pre-launch news conference that the shorter flight path would reduce the crew's fatigue and allow the astronauts to be in top shape for the docking.