Astronauts Michael Foale of the United States and Russian Alexander Kaleri are the eighth crew to have flown to the space station for long-term occupation since the inaugural crew arrived on Nov. 2, 2000. There also have been four short-term missions using Soyuz craft.
Applause broke out at Mission Control outside Moscow after the docking Monday morning.
Pedro Duque of Spain, a European Space Agency astronaut traveling with Foale and Kaleri, is to remain aboard the station for eight days and return on Oct. 27 with American Ed Lu and Russian Yuri Malenchenko, who have been aboard since April 28.
The mission is the second time a Russian Soyuz has taken an American to the space station since the U.S. space shuttle program was grounded after the Feb. 1 disintegration of the shuttle Columbia as it was approaching Earth.
The docking was done automatically, but Lu and Malenchenko nevertheless went to sleep early Sunday to prepare for the event, Russian Mission Control spokesman Valeri Lyndin said.
"It's necessary for the crew to collect their strength," he was quoted as telling the ITAR-Tass news agency.
NASA now depends on Russia to keep its astronauts flying. The Russian Soyuz, whose primary role was to serve as an emergency evacuation craft for the station, is now the only ship capable of carrying crews to and from the 16-nation space outpost.
Foale will become the first American to have served on both the ISS and its predecessor, the Russian Mir.
Malenchenko will become the first person to have left the planet single and return to a wife. He was married in August while in orbit.