The exploration company will buy back shares from January 23 and extinguish them.
The purchase may include a part of the 10.3 per cent stake held by former promoter Cairn Energy Plc.
Cairn India, which is sitting on a cash pile of about $3 billion, received shareholder approval to buy 17.09 crore (170.9 million) shares, or 8.9 per cent of the equity, from the open market at not more than Rs 335 apiece, a public notice said.
The buyback will be open until July 22, the notice said.
After completion, Agarwal's Vedanta Group ownership in Cairn India will rise to 64.53 per cent from 58.76 per cent.
Separately, London-listed Vedanta Resources Plc said it received 99.89 percentage of votes in favour of potential participation of Cairn Energy in the proposed buyback at a shareholder meeting held on Monday.
UK's Cairn Energy sold a majority stake in Cairn India to the Vedanta Group at Rs 355 a share, a level not seen in the past year.
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