The Rangers signed Murphy to a minor-league contract Monday that includes an invitation to spring training camp.
Murphy signed a one-year contract with Japan's Hokkaido Nippon Ham Fighters on Tuesday, Robert Murray of FanSided.com reports.
Murphy was reassigned Tuesday to the minor-league side of Twins camp, Do-Hyoung Park of MLB.com reports.
Jon Heyman of the New York PostMurphy signed a minor-league contract with the Twins on Tuesday, which includes an invitation to spring training, Jon Heyman of the New York Post reports.
Murphy cleared waivers and was outrighted to Triple-A Rochester on Wednesday, Mark Zuckerman of MASNSports.com reports.
Murphy was designated for assignment by the Nationals on Saturday.
Murphy tossed a scoreless inning in Tuesday's Grapefruit League finale against the Mets.
Murphy (0-3) was tagged with the loss in relief Saturday against the Reds after allowing one run on one hit across 1.1 innings, fanning two.
The Nationals will promote Murphy from Triple-A Rochester ahead of Tuesday's game in Miami, Jesse Dougherty of The Washington Post reports.
Murphy was designated for assignment by the Blue Jays on Wednesday.