An independent committee, formed to review and evaluate the proposal, has indicated to Volcan Investments that it supports the offer and intends to recommend a firm offer to Vedanta's shareholders. Volcan currently holds about 66.53 per cent of Vedanta.
The offer of 825 pence per share represents a 27.6 per cent premium to London-listed Vedanta's close on Friday of 646.8 pence.
In addition to the offer price, shareholders will also be entitled to receive a previously announced dividend of 41 cents per Vedanta share, the company said, adding that this would boost the offer price to 856 pence per share.
Indian industrialist Agarwal said last year he does not intend to keep Vedanta in family hands and would withdraw from the group in the next few years.
Agarwal is also Anglo American's biggest shareholder with a nearly 20 per cent stake through Volcan.
Agarwal earlier this year played down speculation that he is seeking a tie-up with Anglo.
Vedanta has come under increased scrutiny in India since police opened fire on protesters, killing 13, at a demonstration against a copper smelter in May. The smelter has since been shut down.