The trade finalizes the compensation the Red Sox received for allowing Theo Epstein to join the Cubs as president of baseball operations.
"I am pleased that the Cubs and Red Sox have resolved this matter," said baseball commissioner Bud Selig in a statement. "It has always been my preference that clubs resolve matters like this amongst themselves, as they understand their unique circumstances better than anyone else could."
Selig had threatened to become involved if the teams could not work out compensation terms.
"Though the matter required time, both clubs demonstrated professionalism throughout their discussions, and I appreciate their persistence in finding common ground."
The 26-year-old Carpenter made his MLB debut with the Cubs in 2011, posting a 2.79 earned run average over 10 relief appearances. The right-hander also combined for 32 games between Chicago's Double-A Tennessee and Triple-A Iowa clubs last year, going 3-4 with two saves and a 5.91 ERA.
Originally selected by the Cubs in the third round of the 2008 draft, Carpenter has a 21-19 record with two saves and a 3.62 ERA in 96 career minor league games (60 starts) in Chicago's system.
The Red Sox also placed right-handed pitcher Bobby Jenks on the 60-day disabled list as he recovers from back surgery, which took place on December 30.
Jenks went 2-2 with a 6.32 ERA for Boston last season. He was limited to just 19 games due to three stints on the disabled list.