Australian Arts Minister Mitch Fifield handed over a 900-year-old stone statue of Goddess Pratyangira and a third century rock carving of worshippers of the Buddha to Tourism Minister Mahesh Sharma at Canberra-based National Gallery of Australia (NGA).
The ceremony was also attended by Indian High Commissioner Navdeep Suri. The ceremony took place in the gallery which houses almost 5,000 pieces of Asian art.
The NGA had bought the two pieces from disgraced art dealer Subhash Kapoor in 2005. Mr Kapoor is currently lodged in Trichy Central Prison.
Last year, the NGA research team examined new photographic evidence from the French Institute of Pondicherry that indicated a sculpture of Goddess Pratyangira which was bought for USD 247,500 was in India in 1974.
This contradicts the dealer-supplied provenance, suggesting the NGA was supplied with false documentation and it was likely to have been illegally exported from India. It is believed that the work has now been reported missing to the Idol Wing of the Tamil Nadu Police, NGA said.
The Buddha carving was bought for USD 595,000 and the NGA was provided with and had verified new photographic evidence that indicates the sculpture was in India as late as the 1990s.
"This new evidence means the NGA cannot legally or ethically retain these works, and returning them to India is unquestionably the right thing to do," Gerard Vaughan, NGA Director said, adding "We have been working closely with the Archaeological Survey of India (ASI) and the Indian High Commissioner in Australia to find the best outcome".
Mr Sharma will be taking another piece of artwork called 'seated Buddha."
He thanked the Australian government for the gesture and lauded the role of Mr Suri on working towards building the bilateral relation.
Mr Sharma said the artworks will now be placed in National Museum in India.
The Australian minister said that the important decision to remove the artworks from the gallery was taken after the findings of the NGA.
Mr Fifield said there were at least seven more objects in questions which the NGA is currently investigating.
In 2014, former Australian Prime Minister Tony Abbott handed over to Prime Minister Narendra Modi two antique statues of Hindu deities which were stolen from temples in Tamil Nadu before being bought by art galleries in Australia.