Iranian-born US citizen and telecoms entrepeneur, Anousheh Ansari, paid $A26 million dollars for the adventure, becoming the fourth such tourist.
The Russian-made Soyuz rocket left the Russian base carrying a Soyuz TMA-9 capsule and its three passengers: Mrs Ansari, NASA's Michael Lopez-Alegria and Russian cosmonaut Mikhail Tyurin.
The capsule successfully separated minutes later and entered orbit, with docking at the ISS expected on Wednesday.
Mrs Ansari, 40, will spend about eight days aboard the ISS before returning to Earth on September 28 with two of the station's current occupants, Russia's Pavel Vinogradov and American Jeffrey Williams.
Her family shed tears of joy as the Soyuz rocket, powered by 270 tonnes of low-temperature oxygen and kerosene fuel, shot above the Kazakh steppe.
Ms Ansari, who came to the United States with her parents from Iran when she was 16, made a fortune in the US telecoms market and had dreamt for years of going into orbit.
"I feel relieved she's up there," her husband Hamid Ansari said after the blast-off.
"The anticipation is over. It's the beginning of a new chapter in her life. I can't wait to see her come back."
Soyuz rockets became the main workhorses taking people to the ISS after the grounding of the US space shuttle fleet in 2003, an interruption that ended with the successful launch of the shuttle Atlantis last weekend.
In case of mishap, Russian air and naval forces were patrolling near the rocket's launch path over Kazakhstan, Siberia and the Sea of Japan.
Russia rents the Baikonur launch site in the Kazakh steppe from Kazakh authorities.