Sunita along with Yuri Malenchenko of Russia and Japan's Akihiko Hoshide left for the ISS aboard a Russian spacecraft Soyuz TMA-05M at 0810 IST.
46-year-old Williams will be a flight engineer on the station's Expedition 32 crew and will become commander of Expedition 33 on reaching the space station.
Williams, whose father hailed 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 holds the record of the longest spaceflight (195 days) for female space travellers.
She received a master's degree from the Florida Institute of Technology in 1995.
In the space, Williams and her team of astronauts plan an orbital sporting event to mark the Summer Olympics in London.
