The reigning World Series champions also offered 2017 contracts to right-handed pitchers Jake Arrieta, Justin Grimm, Hector Rondon and Pedro Strop.
Duensing's contract is for $2 million, according to a person with knowledge of the deal. The person spoke on condition of anonymity because the team did not disclose terms Friday.
Duensing went 1-0 with a 4.05 ERA in 14 relief outings for Baltimore last season. He pitched the previous seven seasons with Minnesota.
For his career, he is 42-37 with a 4.13 ERA in 368 appearances, 307 of which have come in relief.
Chicago has holes to fill in the bullpen this offseason, and Duensing could help. Left-hander Travis Wood and righty Trevor Cahill, two effective relievers with starting experience, became free agents along with right-hander Joe Smith and closer Aroldis Chapman.
Left-handed pitchers Gerardo Concepcion and Zac Rosscup, right-handed pitcher Conor Mullee and infielder Christian Villanueva were non-tendered on Friday.
Chicago's 40-man roster stands at 35 players.
