Red Sox general manager Ben Cherington would not comment on Dempster at a news conference to announce the signing of outfielder Shane Victorino. "We're engaged with a pitcher. That's all I can say at this point," Cherington said, without mentioning Dempster by name.
But a few hours later the sides completed the framework of a deal, the two people familiar with the talks said. They spoke on the condition of anonymity because the agreement was pending a physical.
Dempster would help a rotation led by Jon Lester and Clay Buchholz, promising young pitchers coming off subpar seasons. At the other end of the staff are Franklin Morales and Felix Doubront; pitchers the Red Sox hope can develop into dependable starters. John Lackey returns after missing last season due to elbow ligament-replacement surgery.
Dempster, 12-8 with a 3.38 ERA this year, gives the Red Sox a reliable pitcher who has thrown more than 200 innings for four of the past five seasons. He was 5-5 with a 2.25 ERA with the Chicago Cubs this year before being traded to Texas. He was 7-3 with a 5.03 ERA for the Rangers.
Boston hopes he will be an improvement over Josh Beckett, who was 5-11 with a 5.23 ERA before he was traded to the Los Angeles Dodgers in a deal that conceded the 2012 season while clearing $250 million in future salaries. Daisuke Matsuzaka, who arrived in Boston to international fanfare, was 1-7 with an 8.28 ERA last season while battling injuries.
Dempster, 35, has a 124-124 record and a 4.33 ERA in a 15-year big league career, most of it with the Marlins and Cubs.