Peters agreed to terms with Latvian club Dinamo Riga of the KHL on Friday.
Peters was acquired from Arizona on Wednesday along with Justin Hache in exchange for Brendan Ranford and Branden Troock.
Peters was reassigned to the minors Thursday.
Peters was recalled from the minors Friday.
Peters was reassigned Tuesday to the minors, Sarah McLellan of the Arizona Republic reports.
Peters replaced a struggling Louis Domingue in the second period of Friday's game against the Ducks, picking up 10 saves on 12 shots in the eventual 5-1 loss.
Peters allowed four goals on 34 shots during Tuesday's loss to the Devils.
Peters will start between the pipes in Tuesday's road game against the Devils.
Peters saved 23 of 24 shots after replacing Louis Domingue in the second period of a 5-2 loss to the Canadiens.
Peters was called up to the Coyotes on Wednesday, Sarah McLellan of the Arizona Republic reports.