46-year-old NASA astronaut Williams, Russian Soyuz Commander Yuri Malenchenko and Japan Aerospace Exploration Agency flight engineer Akihiko Hoshide started their two-day voyage at O8.10 am IST for a four-month mission on the International Space Station (ISS).
The Soyuz TMA spacecraft is due to dock with the ISS's Zvezda service module at 10.22 am IST on Tuesday.
Born in Euclid in Ohio and raised in Massachusetts, Williams, who had earlier lived and worked aboard the ISS for six months in 2006-07, will further extend the record for the longest stay in space for a woman astronaut.
Ahead of the launch, she told reporters that the test mission laid the ground for a long-standing friendship and collaboration in the space programme.
She also said that she will be excited to watch the London Summer Olympics from the station and put a much more global perspective on the mega sporting event beginning July 27.
Williams, a flight engineer on the station's Expedition 32 crew, will take over as commander of Expedition 33 on reaching the space station.
The trio will join the current ISS occupants - Russian cosmonauts Gennady Padalka and Sergei Revin and NASA astronaut Joe Acaba, who have been in orbit since May 17.
The six crew members will work together for about two months. Acaba, Padalka and Revin are scheduled to return to Earth on September 17. (More)
