Peterson signed a minor-league contract with the White Sox on Thursday, Brandon Warne of ZoneCoverage.com reports.
Peterson cleared waivers and was outrighted to Triple-A Louisville on Tuesday.
Peterson was claimed off waivers by the Reds on Sunday.
Peterson was claimed off waivers by the White Sox on Sunday.
Peterson was designated for assignment Sunday.
Peterson will be limited for a few days with a leg issue, the Seattle Times' Ryan Divish reports.
Peterson is expected to begin the season as the starting first baseman at Triple-A Tacoma, Bob Dutton of the Tacoma News Tribune reports.
Peterson was added to the Mariners' 40-man roster on Friday.
Peterson, 24, is slashing .305/.352/.549 with five homers and a 24:5 K:BB in 82 at-bats since being promoted to Triple-A Tacoma.
Peterson has been promoted to Triple-A Tacoma, seattlepi.com reports.