Apollo said Wednesday that 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 $6.6 billion.
Their tire brands include Apollo, Cooper, Roadmaster and Vredestein.
Under the terms of the deal, Cooper shareholders will receive $35 per share in cash. The price represents a 42 percent premium over Cooper's Tuesday closing stock price.
Cooper shares jumped $9.95, or 41 percent, to $34.52 in morning trading Wednesday.
Based on the company's 63.3 million outstanding shares, the deal is worth about $2.22 billion. The companies valued the sale at about $2.5 billion.
Apollo Chairman Onkar Kanwar said the combined company will be uniquely positioned to serve both large, established markets, such as the U.S. and Europe, as well as fast-growing markets such as India, China, Africa and Latin America.
Findlay, Ohio-based Cooper said the deal is in the best interests of its shareholders.
Apollo didn't say if any jobs would be eliminated as part of the sale, but said it expects Cooper to continue to operate out of its facilities around the world.
In addition, Cooper executives are expected to continue leading the company and Cooper will continue to recognize its labor union and honor the terms of contracts currently in effect. It also plans to generally maintain pay and benefit levels for non-union employees.
With a history dating back to 1914, Cooper currently employs nearly 13,000 people around the world and has manufacturing plants on three continents. Its brands include Cooper, Mastercraft, Dean, Starfire, Roadmaster and others.
Its 2012 revenue totaled $4.2 billion. Last month, the company said its first-quarter profit more than doubled to $56.1 million, as lower raw material and manufacturing costs more than offset a double-digit drop in sales stemming from lower global demand and tough economic conditions.
The company said at the time that it expected that weakness would continue through the current quarter and possibly beyond.
Apollo, founded in 1972, produces premium and mid-tier tires in a variety of brands including Apollo and Vredestein.
The sale, which remains subject to Cooper shareholder and regulatory approvals, is expected to close in the second half of this year. When that happens, Cooper will become a privately held company and cease trading on the New York Stock Exchange.