The 37-year-old right-hander spent the last two seasons with Texas, and Rangers general manager Jon Daniels said Thursday that he had tried to re-sign him before Uehara decided to accept Boston's offer.
"We would have liked to have him back,'' Daniels said. "We made an offer early in the process.''
Uehara had a 1.75 ERA in 37 relief appearances this year, holding batters to a .160 average.
Earlier in the week, Texas agreed to an $8 million, two-year contract with Joakim Soria, who is coming back from elbow surgery.
"Once we signed Joakim, we held back from making other proposals to relievers right now, just `til we know what's going on with the rest of the club,'' Daniels said. "It's still an area that we need to continue to address, and that's why we tried to do it a little on the cheaper side while we look at some of these other things.''