The deal is reported to be for over 2 billion dollars.
Apollo says the combined company will be one of the world's largest tire makers, with a strong presence across four continents and combined 2012 sales of 6 point 6 billion dollars.
Under the terms of the deal, Cooper shareholders will receive $35 per share in cash. Cooper says the deal is in the best interests of its shareholders.
The sale, which remains subject to Cooper shareholder and regulatory approvals, is expected to close in the second half of this year.