Peavy, who will wear No. 44, has been officially added to the roster. The veteran right-hander will throw a side session Thursday in preparation.
"He's excited and he's looking forward to the challenge and the opportunity here," said Farrell, who spoke with Peavy when he arrived at the ballpark Thursday. "He's excited to be here in Boston."
Peavy said he was thrilled that the arc of his career has taken him to Boston.
"The opportunity I've been given, I can't ask for anything more to come to a team in first place with a realistic chance this year of being a world champion, which why we all play the game," Peavy said.
"To compete in the postseason would be a dream come true. I know that's what a lot of guys here expect. I expect to do it, and be a contributing factor going forward."
The Red Sox acquired Peavy on Tuesday as part of a three-team, seven-player trade that included sending infielder Jose Iglesias to the Detroit Tigers. Peavy's presence gives Boston's rotation more stability while fellow starter Clay Buchholz (neck strain) continues to rehab in hopes of returning at some point this season.
"What I can add? I think I can win," Peavy said. "I think I can still be a pitcher who goes out every fifth day and can give my team a chance to win. I promise you this: No one expects more of me than myself, and I wouldn't be playing if I still didn't think I could be a contributing factor to this ballclub."
To make room for Peavy, the Red Sox optioned right-handed reliever Jose De La Torre to Pawtucket. Given Boston's 15-inning marathon win over the Seattle Mariners on Wednesday night, the Red Sox also optioned pitcher Brandon Workman to Pawtucket and recalled pitcher Steven Wright.
Workman, who has made three starts for the Red Sox, was scheduled to move to the bullpen with the addition of Peavy, but would not have been available in relief until Sunday after starting Tuesday's game.
"It's a unique set of circumstances that we had to make two roster moves," Farrell said.
If Thursday's starter, Ryan Dempster, ran into trouble early in the game, the Red Sox needed a pitcher who could be stretched out, which is why Wright was recalled.
Prior to the Red Sox making the roster moves, Farrell spoke with Workman and explained the situation.
"He's aware of that," Farrell said. "Unfortunate circumstances [Wednesday] night takes him off the roster but he understands the reason why."
The earliest Workman would be back on the mound for the Triple-A PawSox would be Sunday in a bullpen role. He will work multiple innings as a reliever for Pawtucket in order to remain stretched out.