Callaway is replacing Terry Collins, who it was announced in October will soon begin serving as a special assistant to Sandy Alderson's front office.
The team's previous hitting coach, Kevin Long, interviewed to replace Collins, after which he signed to join Dave Martinez's bench as hitting coach for the Nationals.
Dan Warthen was dismissed as Mets pitching coach when Collins stepped down. He has since been hired by the Rangers where he will serve as assistant pitching coach to Doug Brocail.
The team has not yet announced if Tim Teufel will return to the organization.