Shares of the U.K.-based pharma heavyweight jumped 12% to $1.78 a share.
In its pending deal with Cuyahoga and Summit counties, Mallinckrodt agreed to pay $24 million cash and $6 million of generic products, including products for addiction treatment.
In exchange, "all named Mallinckrodt entities will be dismissed with prejudice from the lawsuit," the company said in a statement.
Mark Cassey, the pharma company's general counsel, said the company would now turn its attention to reaching a "global resolution" of the remaining opioid lawsuits it faces.
Shares of Mallinckrodt dropped sharply on Thursday after reports said the company was considering filing for bankruptcy as a way of dealing with a separate $15 million group of opioid-related claims against its Questcor unit.
Mallinckrodt in June agreed with the Department of Justice to resolve claims that sales representatives for Questcor paid kickbacks to doctors -- in the form of lavish dinners and entertainment -- to write prescriptions of the company's H.P. Acthar Gel drug from 2009 to 2013.