Cordell was released by the Phillies on Thursday, Andersen Pickard of MLBDailyDish.com reports.
Cordell joined the Phillies on a minor-league deal in late April, source reports.
Cordell was designated for assignment by the Mets on Monday.
Cordell had his contract selected by the Mets after Game 1 of Saturday's doubleheader against the Nationals, Tim Healey of Newsday reports.
Cordell cleared waivers and was outrighted to the Mets' alternate training site, Tim Britton of The Athletic reports.
Cordell was designated for assignment by the Mets on Wednesday, Justin Toscano of The Bergen Record reports.
Cordell was recalled to the majors Wednesday, Anthony DiComo of MLB.com reports.
The Mets re-signed Cordell on Monday and announced he would be included in the team's 60-man player pool.
Cordell has made a good first impression on his new teammates in camp after being signed to a minor-league contract by the Mets in January, Anthony DiComo of MLB.com reports. "He's showing a little bit of everything -- drop down a bunt, oppo home run, he threw a guy out, diving catch," said Michael Conforto. "He's done a little bit of everything."
Cordell signed a minor-league contract with the Mets on Thursday as a non-roster invitee, Anthony DiComo of MLB.com reports.