Data from the Chandrayaan-1 spacecraft also suggests water is still being formed on its surface.
It is believed that the water is concentrated at the poles and possibly formed by the solar wind.
The finding was made after researchers examined data from three separate missions to the moon.
The reports, to be published in the journal Science on Friday, show that the water may be moving around, forming and reforming as particles become mixed up in the dust on the surface of the moon.
Dr Mylswamy Annadurai, the mission’s project director at the Indian Space Research Organisation in Bangalore, told The Times: “It’s very satisfying.
“This was one of the main objectives of Chandrayaan-1, to find evidence of water on the Moon.”
The unmanned craft was equipped with Nasa’s Moon Mineralogy Mapper, designed specifically to search for water by picking up the electromagnetic radiation emitted by minerals.
The M3, an imaging spectrometer, was designed to search for water by detecting the electromagnetic radiation given off by different minerals on and just below the surface of the Moon.
Unlike previous lunar spectrometers, it was sensitive enough to detect the presence of small amounts of water.
M3 was one of two Nasa instruments among 11 pieces of equipment from around the world on Chandrayaan-1, which was launched into orbit around the Moon in October last year.
Carle Pieters of Brown University in Rhode Island and colleagues reviewed data from Chandrayaan-1 and found spectrographic evidence of water. The water seems thicker closer to the poles, they reported.
"When we say 'water on the moon,' we are not talking about lakes, oceans or even puddles. Water on the moon means molecules of water and hydroxyl (hydrogen and oxygen) that interact with molecules of rock and dust specifically in the top millimetres of the moon's surface," Pieters said in a statement.
Scientists said the breakthrough would change the face of lunar exploration.
