Blewett signed a minor-league contract with the White Sox on Saturday.
Blewett is expected to report to Triple-A Charlotte once he completes his ramp-up program at the White Sox's spring training facility in Arizona. The 26-year-old right-hander made five MLB relief appearances with the Royals between the 2020 and 2021 seasons, giving up three earned runs on nine hits and six walks over eight career innings.