Source: Koji Uehara to Red Sox

The Boston Red Sox and free-agent reliever Koji Uehara struck an agreement on a one-year, $4.25 million deal Thursday, according to a major league source.

The deal is pending a physical.

The 37-year-old Uehara was one of the best relievers in baseball last season for the Texas Rangers, sporting a 1.75 ERA, a 0.64 WHIP and 43 strikeouts (compared to just three walks) in 36 innings. His 14.3 strikeout-to-walk ratio was the third best in the majors since 1900 (minimum 35 innings pitched), according to ESPN Stats & Information. Only Dennis Eckersley was better.

The right-handed Uehara made $4 million last season for the Rangers, missing more than a month with a lat injury.

Uehara has pitched in the majors the past four seasons after a successful career in Japan. He pitched with the Baltimore Orioles from 2009-11 before being dealt to the Rangers in midseason.

Uehara was used primarily as a setup man for the Rangers, with 36 of his 38 appearances coming in the seventh inning or later in 2012.

Before departing Nashville's winter meetings Thursday morning, Red Sox general manager Ben Cherington told reporters the team had made progress on an acquisition that had not been previously reported.

"Last night we were working on a couple of things, but nothing ready to announce," Cherington said. "We made progress on one thing, but it's not quite teed up yet."

Rangers general manager Jon Daniels said the club made an offer to Uehara at the GM meetings last month. But once the Rangers signed Joakim Soria this week, they decided to back off the free-agent relief market until other parts of the club were settled.

Uehara joins a Red Sox bullpen that is already one of the strengths of the team. Besides Uehara, closer Andrew Bailey and the up-and-coming Junichi Tazawa (45 strikeouts, 5 walks and a 1.43 ERA in 44 innings last season), the relief corps could also include Alfredo Aceves and lefty specialists Andrew Miller (held lefties to a .145 average in 2012) and possibly Franklin Morales, who could also be considered for a spot in the rotation.

Mark Melancon and Daniel Bard, both one-time late-inning studs who struggled in 2012, could also be contributors if they can get past shaky seasons and regain their form of old.

ESPNDallas.com's Richard Durrett contributed to this report.