CHICAGO — The Cubs and the Red Sox announced a deal today that settles their dispute over what Boston should get after executive Theo Epstein left for Chicago.

The Cubs are sending right-handed reliever Chris Carpenter and a player to be named later to the Red Sox for a player to be named.

Epstein became Chicago’s president of baseball operations and got a five-year, $18.5 million deal in October. The teams were not able to agree on compensation and submitted arguments to Commissioner Bud Selig.

Epstein, however, said the two teams settled things themselves.

“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,” he said in a statement released by the team. “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.”

The 26-year-old Carpenter was a third-round draft pick by the Cubs in 2008. He made 42 relief appearances between Double-A Tennessee, Triple-A Iowa and the Cubs. He spent four years in the minors before seeing his first major league action last season, when he posted no record and a 2.79 ERA in 10 appearances.

The Red Sox bullpen is in a state of flux and it’s one of Bobby Valentine’s chief concerns this spring. Andrew Bailey was acquired from Oakland in December, and the overriding thought is that he will replace Jonathan Papelbon. But Valentine has been noncommittal with all roles so far. He’s more concerned with adding to the depth, working all of the pitchers out and seeing what he has in a few weeks.

Cubs general manager Jed Hoyer said both teams were happy the dispute was “behind us.”

“Now we can just move forward with the spring without worrying about the compensation,” he said in Mesa, Ariz., at Chicago’s spring training complex. “Chris is a very good reliever. 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, and this doesn’t change that.

“I hope Chris has a lot of success over there. Obviously the Cubs are really excited about the new management team with Theo leading it, so there was a price to be paid for that.”

As for the players to be named later, Hoyer called it a “procedural” thing to meet MLB transaction rules.

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