The finds were made on Saturday beneath the debris of a demolished government office building in the village of Kolappakkam, just south of the southern city of Madras, T Satyamurthy, the region's top government archaeologist, told The Associated Press.
"The discovery is very important evidence of the strong diplomatic, religious and trade relations between India and Southeast Asia more than a thousand years ago," Satyamurthy said by telephone from Madras.
The site lies close to a temple of Lord Shiva, a major Hindu god, and must have been part of the temple premises in ancient times, he said.
The granite inscriptions, written in the Tamil language, say a king of the Srivijaya dynasty from the island kingdom of Sumatra - part of modern-day Indonesia - made a pilgrimage to the temple, where Shiva is worshipped in an incarnation known as Lord Agastheeshwara.
The Buddhist Srivijaya monarchs also worshipped Lord Agastheeshwara, Satyamurthy said.
The writings also said the king purchased land locally and donated them to the temple.
The inscriptions identify the king only by his titles and further research is needed to establish his identity among the Srivijaya kings of that period, he said.
The meter-tall (three-feet-tall) stone statues show Buddha with more east Asian facial features and in a meditative pose, suggesting they must have been brought by the visiting king, Satyamurthy said. Buddha was born Prince Siddhartha in India.