After four weeks of interstellar travel, the spacecraft completed its Lunar Orbit Insertion (LOI) as planned, the Indian Space Research Organisation (ISRO) said in a statement.
The insertion "was completed successfully today at 0902 hrs IST (0332 GMT) as planned, using the onboard propulsion system. The duration of manoeuver was 1738 seconds," the national space agency said.
India is seeking to become just the fourth nation after Russia, the United States and China to land a spacecraft on the Moon.
If the rest of the mission goes to plan, the Indian probe will land on the lunar South Pole on September 7.
Tuesday's insertion was one of the trickiest operations in the mission because if the satellite had approached the Moon at a higher velocity it would have bounced off and got lost in deep space.
And had it approached at a slow velocity, the Moon's gravity would have pulled it towards it, causing a crash.
Chandrayaan 2, or Moon Chariot 2, lifted off from India's spaceport at Sriharikota in southern Andhra Pradesh state on July 22.
ISRO says the mission will help scientists to better understand the origin and evolution of the Moon by conducting detailed topographical studies, mineralogical analyses and a host of other experiments.
About $140 million was spent on preparations for the probe's mission -- a much smaller price tag compared to similar operations by other countries.