Kelly, 30, posted a 4.39 ERA and had 57 holds and two saves in 73 appearances last season out of the Red Sox bullpen. He allowed just four hits while shutting out the Dodgers in five World Series appearances. He also had 10 strikeouts in six innings against the Dodgers.
His deal is pending a physical and the clubs have not confirmed the trade. Kelly is expected to assume a similar setup role in the Dodgers bullpen. The right-hander began his career with the St. Louis Cardinals, before being traded to the Red Sox in 2014.
Kelly owns a 3.87 ERA and a 43-25 record in 250 appearances during his seven-year Major League Baseball tenure.