The Red Sox acquired Bedard just moments before Sunday's non-waiver Trade Deadline expired.
He will report to Fenway Park on Tuesday, at which point he'll get the chance to get familiar with manager Terry Francona and his new teammates. Bedard is also expected to meet with the Boston media.
"I talked to him yesterday a little bit, before we got to the airport," said Francona. "Yeah, he was terrific. He said he's looking forward to it, and we talked about his day to pitch so he can get himself sort of settled when he gets here and everything. We're looking forward to getting him going."
With the addition of Bedard, the Red Sox will wait until next week to subtract someone from the five-man rotation.
For now, Bedard will simply supplement the existing rotation amid a juncture when the Red Sox don't have a day off until Aug. 11.
Josh Beckett will pitch Tuesday, and Tim Wakefield will make his second attempt at win No. 200 on Wednesday.
When Bedard makes his Boston debut, he will be on a pitch count. The lefty only lasted 57 pitches in his first start back from the disabled list on July 29.
Andrew Miller will be available out of the bullpen Thursday to piggyback Bedard.
The addition of Bedard means that Jon Lester can now pitch Friday against the Yankees instead of in the Indians series. John Lackey and Beckett will finish the three-game weekend showdown against New York.
If Miller isn't needed in the bullpen on Thursday, he will open the road trip at Minnesota on Monday. Otherwise, Wakefield will start Monday, followed by Miller on Tuesday.
Once the Red Sox get to Seattle for the off-day, Francona will evaluate how the rotation best fits together.
"We don't have that day off until we go to Seattle, and then we have two in about a four-day span," Francona said. "Obviously, the six-man thing doesn't help then. We'll get to that off-day, and then we'll probably mix and match a little bit and we'll see what we feel puts us in our best position. For the time being, they can all use an extra day."