Free-agent Ryan Dempster reached a two-year, $26.5 million agreement Thursday with the Boston Red Sox, a baseball source told ESPN.com.
The deal is pending a physical.
Dempster turned down a pair of two-year offers worth between $25 million and $26 million from the Red Sox and Royals last week, the source said, and was believed to be seeking a third year.
The 35-year-old Dempster had logged at least 200 innings for the Cubs from 2008-11, and had a 2.25 ERA in 16 starts last season before being traded to the Texas Rangers. Two stints on the disabled list in 2012 prevented him from reaching 200 innings for a fifth year.