Baldwin filed the suit against the Bodyguard star in December 2010.
In the suit, he claims Costner scammed him and a friend out of $18 million (£11 million) in a deal with BP for oil-separating centrifuges after the April 2010 spill.
The Huffington Post reports that Baldwin and his friend Spyridon Contogouris say they didn't know about the deal when Costner convinced them to sell back their shares in the product for $1.4 million (£910,000) and $500,000 (£325,000) respectively to Ocean Therapy Solutions, the company marketing the centrifuges.
It is thought that Costner eventually sold the machine to BP for $52 million (£33 million).
Costner, who recently starred in the record-breaking drama mini-series Hatfields & McCoys, has yet to comment on the lawsuit.