The Red Sox went 69-93 last season, their worst record in more than four decades.
The 35-year-old Dempster, who got a two-year, $26.5 million deal from the Red Sox, certainly represents an upgrade over the types of pitchers the team signed a year ago to supplement its staff, injury risks such as Aaron Cook and Vicente Padilla. He has pitched 200 or more innings in four of the past five seasons, and in 2012, when he fell short of that figure, he was in considerable demand before Texas nabbed him at the trade deadline, ranking second in the National League with a 2.25 ERA in 16 starts for a struggling Cubs team.
The Cubs, Brewers and Royals all took runs at Dempster this offseason before he signed with the Red Sox, who showed as much interest in him as anyone, the veteran said Wednesday. He turned down their first offer of two years and $25 million, but when it became apparent he was not going to get a three-year deal anywhere, he took Boston's upgraded offer.
Given his track record, the 15-year veteran with a .500 lifetime record (124-124) and a 4.33 career ERA figures to slot third in the Red Sox' rotation behind Jon Lester and Clay Buchholz and ahead of John Lackey and Felix Doubront.
"I've said it before and I'll say it again,'' Red Sox general manager Ben Cherington said Wednesday. "We're excited to have Ryan Dempster, but we believe the performance of the guys who are already here is going to have a bigger effect on the overall rotation than any one player we add. But I think he is a really good fit for a lot of reasons.''
Dempster, who began his career with the Florida Marlins in 1998, will be starting a season with an American League team for the first time. He struggled initially after his trade to Texas, giving up eight earned runs in two of his first three starts but then went 5-0 with a 1.91 ERA in his next five, striking out 36 batters in 33 innings. He wound up with 70 strikeouts in 69 innings for the Rangers, and his 9.1 strikeouts per nine innings with Texas was the highest ratio of his career.
But Dempster and the Rangers faltered down the stretch, and with the AL West title on the line the last day of the season in Oakland, he couldn't hold onto a 5-1 lead and was knocked out in the fourth inning of an eventual 12-5 A's win. In a dozen starts with Texas, Dempster had a 7-3 record and a 5.09 ERA, though he struck out 70 batters in 69 innings.
The Rangers, choosing to focus on free agent Zack Greinke, did not take a run at Dempster. Because he was traded at midseason, the Rangers were not eligible for draft-pick compensation for Dempster if they made a qualifying offer to him.
Asked to characterize his performance last season, Dempster said Wednesday: "I don't know. Aside from a few starts, I try to define myself as a consistent person, a consistent pitcher. The first half went extremely well, and after a few starts (in Texas), I started to get on a roll."
Dempster pitched at Fenway Park for the first time in 11 years on Aug. 7, and was credited with the win in a 6-3 victory over Lester, one in which the right-hander gave up three unearned runs on six hits in 6 2/3 innings. He also threw seven scoreless innings against the Red Sox at Wrigley Field while still with the Cubs in a 3-0 win over Daisuke Matsuzaka on June 15.
A native of Sechelt, British Columbia, Dempster said he has yet "to figure out" whether he would pitch for Canada in the World Baseball Classic in March.
"My No. 1 goal is to be ready to pitch for the Boston Red Sox,'' he said.