Asarco, formerly known as American Smelting and Refining Company, is an over 100-year old company and is currently the third largest copper producer in the US.
"We are delighted to have reached agreement on this important acqusition, which is a significant milestone for our group," Sterlite's Chairman Anil Agarwal said in a release.
The agreement is subject to the approval of the US Bankruptcy Court for the Southern District of Texas, Corpus Christi Division, the release said.
A Sterlite official told PTI that it would take six to seven months to complete the acquisition.
Asarco, which filed for bankruptcy protection in 2005 following sued for $1 billion over environmental issues, produced 235,000 tonnes of refined copper in 2007.
However, its mines have estimated reserves of five million tonnes of contained copper. Asarco operates mines, mills and a smelter in Arizona. It also has a smelter and refinery in Texas.
For the year ended December 31, 2007, Asarco had reported a revenue of around $1.9 billion.
Sterlite has a capacity of 4,00,000 tonnes per annum (tpa) of copper annode and 240,000 tpa of copper rod in its Silvasa and Tuticorin facilities.