Dow Chemical Co
The sale of the unit, which makes latex, rubber and related plastics, will help the nation's largest chemical maker further bolster its balance sheet following the $15 billion acquisition of Rohm and Haas last year.
Dow had net debt of $19.5 billion at the end of 2009.
The deal also helps Dow move away from commodity chemicals and lets it focus more on the higher-margin specialty chemical sector.
The $1.63 billion price was higher than some analysts had expected. Morgan Stanley's Paul Mann had forecast $1.2 billion. He expects the deal to have minimal impact on Dow's earnings.
Shares of Dow rose 37 cents to $29.06 in midday trading Tuesday.
Bain bid in the second round of the auction for Styron, alongside buyout firms TPG
Reuters had reported that Bain was about to strike a deal.
From the beginning, Styron attracted mostly private equity buyers, which were interested in the unit's cyclical business and deep connection to basic economic fundamentals.
But the auction was a complex one because Dow has numerous contracts with the unit as both a supplier and a customer.
Midland, Michigan-based Dow will have an option to retain a 15 percent stake in Styron. The deal also includes $400 million in supply agreements, where Dow will feed Styron the materials needed to produce its plastics.
The deal is expected to close by August. Based on 2009 data, Styron is forecast to have $3.5 billion in annual revenue.
Styron has a large presence in Belgium but also has several locations elsewhere in Europe and in Asia and Latin America.
Dow has said it is targeting sales of $2 billion in nonstrategic assets this year. Last week it said it had a contingency plan if it was not able to reach that target.
(Reporting by Megan Davies, Ernest Scheyder, Matt Daily and Michael Erman; editing by John Wallace)