Corey was designated for assignment on July 25 so that the Rangers could clear a roster spot for Adam Eaton.
After being recalled from Triple-A on June 9, Corey, 32, put up solid numbers. In 16 outings, he was 1-1 with a 2.60 ERA. Over 17 1/3 innings, Corey registered 13 strikeouts and allowed 15 hits.
"I got my first win [at Fenway] and got my first loss there. I'm excited," Corey said. "I'm going to miss it here. But they're excited to have me. I really wanted to stay in this [playoff race] atmosphere."
To make room for Corey on the 40-man roster, the Red Sox shifted Matt Clement to the 60-day disabled list. The club doesn't plan to activate Corey until Wednesday.
"He pitched against us a couple of times," Red Sox manager Terry Francona said. "He's getting lefties out like crazy. He's got kind of a nice arm. It will be kind of interesting to see him on our ballclub because we liked him with Texas."
Corey was originally a position player before being converted by the Tigers in 1995. He has spent time with in the Minor Leagues with the Diamondbacks, A's, Padres, Dodgers and Cubs and pitched in Japan in 2004.
The Rangers signed Corey as a Minor League free agent on March 29.
The Red Sox have been inconsistent with their middle relief this season, so Corey will have a chance to help remedy that.
Mendoza went 1-5 with a 6.38 ERA in nine starts since being promoted to Double-A Portland in June.
Ian Browne is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.