According to a notice posted on the London Stock Exchange, the Volcan Holdings investment company owned by Agarwal's family now owns 11.44 per cent of the group's capital and voting rights following Tuesday's share purchase.
It is now the second largest shareholder behind South Africa's Public Investment Corporation, which owns more than 13 per cent.
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Agarwal's investment is believed to be worth 1.9 billion pounds ($2.4 billion, 2.2 billion euros). The company's market capitalisation is around 16.4 billion pounds.
Volcan also owns mining competitor Vedanta Resources, which specialises in zinc. Agarwal last month told the FT Global Commodities Summit that he did not intend to seek a seat on Anglo-American's board.