Putnum, a University of Michigan alum, was a former fifth-round draft pick by the Cleveland Indians in 2008 and appeared in 10 major league games for the Indians and the Rockies over the past two seasons.
The 25-year-old right-hander has been used exclusively in relief at the Triple-A level the past two seasons, posting a 4.15 ERA and 12 saves at Colorado Springs last season. In 2011, he had a 3.65 ERA with nine saves at Columbus.
The Cubs freed up 10 spots on the 40-man roster last week. Pitcher Chris Volstad and catcher Anthony Recker were claimed by other clubs, while eight other players were outrighted to Triple-A. Right-hander Manny Corpas, one of the players outrighted, elected to become a free agent.