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.
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 30-year-old 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.