Zvezda's solar panels and several antennae were reported to have unfolded shortly after deployment.
The Zvezda module - the "brain" and living quarters of the ISS - lifted off on a Proton-K rocket at 0456 GMT.
The rocket could be seen soaring into a clear blue sky, trailing a cone of flame.
The Proton's three stages fell away, one at a time, as planned, and within nine minutes of blast-off, the rocket had entered orbit.
Zvezda's solar panels and several antennae were reported to have unfolded shortly after deployment.
Russian and US space agency officials, who had been monitoring the launch on a giant screen at mission control in Moscow, gave loud applause when they knew everything had gone well.
"I feel great joy that our Russian module is in orbit but we still have some worries," said Vladimir Lobachev, director of mission control. "If the docking goes successfully, then we'll celebrate."
Robert Castle Jr, Nasa's flight director for shuttle and station mission operations, described the mood among Russian and US officials as "ecstatic". "It's a major step in both countries' space programs," he said.
Pizza sponsorship
The Russian-built module will orbit the Earth for two weeks before linking up with the embryonic ISS 400 km (250 miles) above the planet's surface.
If Zvezda fails to dock successfully then it is understood a three-man team, known as the "zero crew", currently on standby at Baikonur, will race into space and make the connection manually.
Zvezda has gone up nearly two years behind schedule - a delay that is thought to have cost the multinational space station project as much as $3bn.
The delay has also led to some angry exchanges between Zvezda's engineers and the US space agency Nasa, which has accused Russia of wasting time and resources on the 14-year-old Mir space station.
The US General Accounting office has also accused Russia of failing to meet Nasa safety standards in building Zvezda, saying the module's magnesium and aluminium skin may not provide adequate protection against collisions with space junk and that equipment will fail if cabin pressure is lost.
Russia insists that Zvezda is reliable and that the ISS is a priority. President Vladimir Putin has promised that the country will meet its commitments.
Zvezda's launch costs were partially offset by sponsorship from the American fast food chain Pizza Hut. A large logo advertising the food giant had been placed about halfway up the side of the rocket.
Russian newspaper reports say the advertising has cost Pizza Hut $1m.
Thirteen windows
Zvezda was actually completed last summer but the launch was further postponed after two crashes of Proton rockets - the same kind of vehicle that has lifted the module into orbit.
The first long-stay ISS crew should arrive at the end of October.
The new module will make their lives as comfortable as is possible in the micro-gravity of Earth's orbit.
Zvezda, which means "star" in Russian, will provide air, water, cooling and food for the astronauts, additional electricity for experiments, and a docking port for vehicles coming to and from the station.
Zvezda's main compartment consists of a laboratory, three sleeping areas, a bathroom, galley and exercise facilities. Its 13 windows will provide one of the best views in history.
The ISS currently comprises two modules: the US-built Unity and the Russian module Zarya.
The ISS, a joint venture involving the United States, Russia, Europe, Japan and Canada, is expected to cost $60bn when completed, perhaps by 2005. The first ISS crew is expected to take up station in October under the command of US astronaut William Shepherd.