By Jonathan Stempel

March 3 (Reuters) - A Delaware judge on Monday ordered ITG Brands to pay rival cigarette maker Reynolds American $251.5 million in connection with a Florida tobacco settlement, following ITG's purchase of four cigarette brands from Reynolds a decade ago.

Vice Chancellor Lori Will of the Delaware Chancery Court rejected ITG's argument that the $251.5 million, the full amount Reynolds sought, be reduced by money Reynolds saved because ITG did not join the Florida settlement.

Reynolds is a unit of British American Tobacco BATS.L, while ITG is a unit of Britain's Imperial Brands IMB.L.

The case arose from Reynolds' June 2015 sale of the Kool, Maverick, Salem and Winston brands to ITG, so Reynolds could win regulatory approval for its $25.8 billion purchase of smaller rival Lorillard.

Before the sale, Reynolds had for many years made annual payments to Florida under a settlement to recoup tobacco-related healthcare costs, after the state accused cigarette makers of misrepresenting the addictiveness and health risks of smoking.

But after the sale closed, Reynolds stopped making payments that had been based on sales of the four brands it no longer owned.

Florida then sued Reynolds and ITG, and obtained a judgment requiring Reynolds to make payments unless and until ITG joined the settlement.

Reynolds paid Florida $251.5 million attributable to the four brands for 2015 to 2023.

Will in October 2022 found ITG liable to reimburse Reynolds, leaving the question of how much to pay.

In Monday's decision, Will said it would be "perverse" to reduce ITG's liability by the estimated $112.8 million of "profit adjustment" payments that Reynolds saved because ITG did not join the Florida settlement.

"To reduce Reynolds' damages as though ITG joined the Florida settlement agreement would disincentive ITG from ever doing so," Will wrote.

The companies and their lawyers did not immediately respond to requests for comment. Reynolds is based in Winston-Salem, North Carolina, and ITG is based in Greensboro, North Carolina.

(Reporting by Jonathan Stempel in New York; Editing by Richard Chang)

((jon.stempel@thomsonreuters.com; +1 646 223 6317; Reuters Messaging: jon.stempel.thomsonreuters.com@reuters.net))