The right-handed Wheeler grew up in Warwick, R.I., and has spent his 11-year career with the Rays, Mets and Astros.
"I'm very excited," Wheeler told MLB.com's Ian Browne via phone Saturday. "I guess there's always been a little part of me that's always wanted to wear the Red Sox uniform, there's no question about that. The first goal was to make it [to the Majors], now that I'm going to have a chance to put that actual uniform on, I'm real excited about it."
Wheeler, 33, agreed to a one-year deal and joins Bobby Jenks in a revamped Red Sox bullpen. Wheeler will be reunited with Carl Crawford, his teammate in Tampa Bay from 2008-10.
The Rangers announced the signing of three players, all of whom will receive big league Spring Training invites: right-hander Seth McClung, outfielder Endy Chavez and infielder Brian Barden. Colorado also added a Spring Training invitee, signing first baseman Mike Jacobs to a Minor League deal.
Adrian Beltre, perhaps the biggest name left on the market, has reportedly received a "significant" offer from the Angels, their owner Arte Moreno told the Los Angeles Times. The Times speculated that the offer is for five years, $70 million, while Beltre is believed to be seeking a six-year, $90 million deal.
Not far up the interstate, the Dodgers are looking at the Hairston brothers, Scott and Jerry, as well as Marcus Thames as candidates for left field, MLB.com's Ken Gurnick reported.
The Twins also welcomed Tsuyoshi Nishioka at an introductory press conference at Target Field on Saturday. Nishioka, who signed a three-year, $9.25 million contract after winning the batting crown and the Japan Series title with the Chiba Lotte Marines last season, had a simple answer when asked about what he expects to bring the Twins next season.
"I believe my job is to step on home plate as much as possible," said Nishioka, who also indicated he's open to playing second base or shortstop next year.