The Cubs and Red Sox will also exchange players to be named at a later date.
The sides had been unable to agree on compensation since Epstein left as general manager of the Red Sox in October. The matter was eventually passed on to commissioner Bud Selig and both sides submitted written arguments to Selig last week. But Epstein indicated Tuesday that the sides finally agreed on their own.
"I am relieved that this process is over and particularly pleased that the teams were able to reach agreement on their own without intervention from MLB," Epstein said in a statement. "I truly hope and believe that this resolution will benefit both clubs, as well as Chris, who is an extremely talented reliever joining a great organization at a time when there's some opportunity in the major league bullpen."
"More than anything, I'm excited that we can all move forward and focus exclusively on getting ready for the season. I wish Chris and the Red Sox nothing but the best in 2012 and beyond."
To make room on the roster for Carpenter, the Red Sox placed reliever Bobby Jenks on the 60-day disabled list as he recovers from back surgery.
Carpenter, 26, made 42 relief appearances combined at Double-A, Triple-A and for the Cubs last season; with Chicago, the right-hander had a 2.79 ERA in 10 relief outings in his first major league action. He is 21-19 with a 3.62 ERA in four minor league seasons.
Carpenter handled the news well.
"Well, as soon as they called me into the coaches' office I kind of had a feeling of what was going on," he said. "I can't say anything bad. I appreciate everything the Cubs have done for me. It's been a great organization the past four years. I'm looking forward to going to Boston and helping them win now."
Carpenter said that players had joked about being included in the compensation and added that "I guess my name will go down in history."
And he'll play for another storied franchise.
"If you're going to pick two teams to play for, why not it be the Cubs and the Red Sox?" Carpenter said. "You can't complain about that."
Sending Carpenter means that the Cubs will not lose a top prospect, such as outfielder Brett Jackson, third baseman Josh Vitters or starting pitcher Trey McNutt. Still, Carpenter had some upside as a hard-throwing middle reliever.
"Yeah, Chris is a very good reliever," Cubs general manager Jed Hoyer said. "He's a difficult guy to lose. I think we all realized we were going to lose something of significant value when Theo came over here. This doesn't change that.
"I hope Chris has a lot of success over there. Obviously the Cubs are excited about the new management team with Theo leading it. There was a price to be paid for it and that price was Chris. I think we all thought that was fair, but he is talented and we wish him luck. Hopefully both sides do well by this agreement."
Red Sox GM Ben Cherington said Boston has scouted Carpenter since his collegiate career at Kent State. The club also scouted him last season at the minor league level and again during the Arizona Fall League.
"We're really happy to have him," Cherington said. "He's a young power-arm reliever who we think has a chance to be a really good big league pitcher. I haven't had a chance to talk to [Carpenter] yet, but I'll get on the horn with him this afternoon and we'll try to get him to Fort Myers as soon as we can."
Cherington was asked why the Red Sox have to send a player to the Cubs.
"This is still a baseball trade," he said. "It's satisfying the compensation issue, but it's still a baseball trade and in any baseball trade there has to be something coming and something going."
Hoyer said he expects the exchange of players to be named to occur by April 15, adding that the discussions were not contentious.
"I think part of the reason it took so long was that there wasn't a lot of precedent for this kind of transaction," Hoyer said. "And I think both sides had a lot of things going this winter. The Red Sox had a lot of things going this winter with a new GM and a new manager. A lot of transactions. We had a lot of things going on. Not to say this wasn't a priority, but the two teams were focused on the on-field things than that. It probably took a little bit of time because of the lack of precedent. But it certainly wasn't because of any animosity.
"We were actually looking at the people involved on the emails last night and we're all really good friends. This process clearly didn't change that. There was no animosity. It was just a process that took a long time in part because we had a lot of things going on."
Cherington supported Hoyer's take on the transaction, calling it a "unique circumstance."
Information from ESPNBoston.com's Gordon Edes and ESPNChicago.com's Doug Padilla was used in this report.