The Cubs officially announced the deal on Monday.
Duensing, a 34-year-old left-hander, went 1-1 with a 2.74 ERA in 68 relief outings for the Cubs last season. He pitched his first seven seasons for Minnesota and spent much of the 2016 season in the minors before earning a late-season promotion to Baltimore. He then joined the Cubs after their 2016 World Series title.
For his career, Duensing is 43-38 with a 4.01 ERA in 436 appearances, 375 of which have come in relief.
Duensing was drafted in the third round by Minnesota in 2005 and made his major league debut in 2009.