The 29-year-old Reed agreed to terms on Saturday, according to multiple reports.
Overall, Reed is 18-21 with a 3.40 ERA and 125 saves over seven seasons with the Chicago White Sox, Arizona Diamondbacks, Mets and Red Sox. He was originally a third-round pick in 2010 by the White Sox out of San Diego State.
Reed will be one of the leading candidates to be the Twins' closer next season, along with fellow recent signee Fernando Rodney. Rodney said at the time of his signing last month that he was told he was going to be the guy in the ninth inning, but his numbers last year (4.23 ERA, 1.19 WHIP) are worse than Reed's.
Rodney, 41, converted 39 of his 45 save chances for the Arizona Diamondbacks in 2017.
Reed received a good deal of time as the Mets' closer last season with Jeurys Familia suspended to start the year and injured in May. Reed converted 19 of his 21 save chances for New York before being dealt to the Red Sox prior to the trade deadline. In Boston, he primarily served as a setup man for All-Star closer Craig Kimbrel.
Minnesota also designated left-hander Buddy Boshers for assignment. Boshers was 1-0 with a 4.89 ERA in 38 games for the Twins last season.
--Field Level Media