Reed, who saved 32 games in his first season with the D-backs last year, was 1-7 with a 4.25 ERA in 62 outings.
Over his four-year career, including three seasons with the White Sox, Reed has gone 9-13 with a 4.20 ERA and 101 saves.
Joey Nowak is a reporter for MLB.com. Follow him on Twitter at @joeynowak. This story was not subject to the approval of Major League Baseball or its clubs.