If Varitek had accepted Boston's offer, he would have been contractually bound to the Red Sox for the 2009 season.
Right-hander Paul Byrd, the only other free agent who was offered arbitration by the Red Sox, also declined.
Varitek is a Type A free agent, meaning the Red Sox will get two Draft picks as compensation should he sign with another team.
Byrd is classified as Type B, which would make the Red Sox eligible for one supplemental round pick if he signs with another team.
Figuring out the catching situation remains a top priority of Red Sox general manager Theo Epstein at the Winter Meetings, which officially start on Monday in Las Vegas.
There's still a chance Varitek -- Boston's starting catcher since 1999 -- will be part of that situation. In fact, an ideal scenario for the Red Sox would be retaining Varitek and acquiring a younger catcher who could ultimately serve as his successor.
"That's a desirable outcome," Epstein said last week. "We also have catchers-in-waiting in the Minor Leagues who are talented, but maybe not quite ready to step into a prominent role right now. We'll see. I'm confident that we'll find a way to end up with a reputable catching core that we hope will not only have us set up for 2009, but also in the future."
Unlike the Varitek situation, when Byrd declined arbitration, it likely signified the end of his time with the Red Sox.
The right-hander doesn't seem to be a fit for a Boston team that already has Josh Beckett, John Lester, Daisuke Matsuzaka, Tim Wakefield and perhaps Justin Masterson or Clay Buchholz in the rotation.
Byrd is likely to find a team that has more of a need for a fourth or fifth starter. The righty was 11-12 with a 4.60 ERA in 2008. He was acquired by the Red Sox in a trade with the Indians in August, and was 4-2 with a 4.78 ERA in eight starts for Boston.
Ian Browne is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.