Sterlite is a top Indian metal and mining firm and a unit of UK-listed firm Vedanta Resources.
Sterlite bid the highest price for Asarco, which is selling off assets in an attempt to avoid bankruptcy.
However, Grupo Mexico, which acquired Asarco in 1999, says it will try to stop the deal from going ahead.
There is an ongoing disagreement over the ownership of Asarco between the Mexican firm and Asarco LLC, a group of creditors.
In 2005, Asarco sought bankruptcy protection after being sued for $1bn for environmental- and asbestos-related charges.
Grupo Mexico says Asarco, which is the third biggest copper manufacturer in the US, could pay off its debts.
India and China have a growing appetite for commodities such as copper and steel as their economies boom.
The deal still requires approval from the US Bankruptcy Court.
But Sterlite was pleased with its deal.
"We are delighted to have reached agreement on this important acquisition" said a spokesman.
BBC
| Buying | Selling | |
| Euro | 1.8970 | 1.9061 |
| Dolar | 1.3926 | 1.3993 |
| Sterlin | 2.3989 | 2.4114 |













