The transaction involves KKR taking over the Australian snacks unit, Arnott's, and the top-selling cookie brand Tim Tam.
The deal also includes a long-term licensing deal that will allow KKR exclusive rights to use some Campbell brands including Swanson and V8 in the Asia Pacific.
Campbell Soup is expected to use the proceeds of the sale to reduce the company's debt.
Earlier this month, Campbell laid off 80 U.S. workers as part of the company's overall plan to restructure, following agitation from activist investor Dan Loeb.
In the year through Thursday's close, shares of Campbell Soup were down 20%. KKR has rallied 31%.
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Constable owns none of the securities listed in this story.