"Everything is perfect," Malenchenko radioed Russia's Mission Control Center in Korolev after docking with the space station. Their Russian spacecraft -- Soyuz TMA-05M -- docked automatically with the Rassvet module at 10:21 IST.
The crew took off to the ISS successfully from Baikonur cosmodrome in Kazakhstan on Sunday for a four-month long mission to the space station. This is the second space mission for Williams. She also holds the record of the longest spaceflight -- 195 days -- for women space travellers.
The crew, which will return home in mid-November, is expected to conduct over 30 scientific missions during their stay aboard the ISS. In space, Williams and her team of astronauts also plan an orbital sporting event to mark the Summer Olympics in London.
Williams and her crewmates will join the three others already living on the space station: commander Gennady Padalka of Russia, his cosmonaut colleague Sergei Revin, and NASA astronaut Joe Acaba, who have all been in space since May.
The six crew members will work together for about two months. Acaba, Padalka and Revin are scheduled to return to Earth on Sept 17. Before they depart, Padalka will hand over command of the station and Expedition 33 to Williams.
The launch and docking of Expedition 32 coincides with the 37th anniversary of the Apollo-Soyuz Test Project, the first docking of an American spacecraft with a Russian spacecraft.
An Apollo spacecraft from Kennedy Space Centre and a Soyuz 7K-TM vehicle from Baikonur Cosmodrome launched on Jul 15, 1975 and docked two days later.
Williams and her colleagues will be aboard the station during an exceptionally busy period that includes two spacewalks, the arrival of Japanese, US commercial and Russian re-supply vehicles, and an increasingly faster pace of scientific research.
Video cameras on the exterior of the space station captured spectacular views of the Soyuz pulling up to the orbiting lab with the bright blue Earth in the background. Williams lived and worked aboard the International Space Station for six months in 2006.
Williams, whose father hails from Gujarat, was selected as an astronaut candidate by NASA in 1998. She was assigned to the International Space Station as a member of Expedition 14 and then joined Expedition 15. She received a master's degree from the Florida Institute of Technology in 1995.
"I'm just looking forward to seeing the full capability of the space station, it's an experiment, not only the things that were doing inside but also all the engineering that has gone into allowing us to dock new vehicles, do space walks, Russian and US. So, it's a pretty complicated vehicle now and Im looking forward to being part of it," Williams said recently.
Meanwhile, in orbit high above the Earth, Expedition 32 Flight Engineer Joe Acaba focused on cleaning the exhaust and intake ducts of the Starboard Crew Quarters yesterday to prepare them for the arrival of new crewmates, NASA said.