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.

No explanation for Napoli signing delay

Nine days after the Red Sox agreed to terms on a three-year, $39 million contract with free agent first baseman/catcher Mike Napoli, there still was no press conference held at Fenway Park.

And there was no explanation for the delay either.

Team officials have been mum on why a deal with Napoli, who arrived in town earlier this week to take a physical exam, has not yet been finalized. Napoli's agent, Brian Grieper, did not return calls Wednesday.

Given Napoli's injury history, it is plausible the Sox are negotiating protection against the 31-year-old being limited by a pre-existing condition. Napoli has played more than 114 games in a season only once in his seven-year major league career and missed a month in 2012 with a left quadriceps strain.

The Red Sox could cite precedent for such a clause. They wrote an opt-out clause into former right fielder J.D. Drew's contract based on previous shoulder injuries and were protected against starting pitcher John Lackey missing last season after Tommy John surgery because of language in his pact dealing with a previous elbow injury.

Without referring specifically to Napoli, general manager Ben Cherington noted last week at the winter meetings that a physical is "an important final step before anything becomes official."

"Sometimes there are surprises," Cherington said. "When you get your hands on someone, something's different. Sometimes the (medical) files aren't complete. You can only review what's in there."