The Reds signed Shaw to a minor-league contract Friday that includes an invitation to spring training, Robert Murray of FanSided.com reports.
The Angels released Shaw on Wednesday.
Shaw signed a minor-league contract with the Angels on Wednesday, Jeff Fletcher of The Orange County Register reports.
Shaw elected to become a free agent Saturday.
Shaw was designated for assignment by the White Sox on Friday.
The White Sox selected Shaw's contract from Triple-A Charlotte on Wednesday, Daryl Van Schouwen of the Chicago Sun-Times reports.
Shaw is expected to be included on the White Sox's Opening Day roster, James Fegan of SoxMachine.com reports.
Shaw signed a minor-league contract with the White Sox on Saturday and received an invitation to major-league spring training.
Shaw picked up the save in Thursday's 3-1 victory over the Diamondbacks, striking out one over a perfect inning.
Shaw earned a save against the Yankees on Monday, allowing one hit and striking out four batters over two scoreless innings.