Davis was hitting coach for Oakland manager Bob Melvin (2012-14) and Boston manager John Farrell (2015-17) before moving to the Cubs under manager Joe Maddon.
Davis was fired in October. The Cubs were 22nd among the 30 teams, with 167 home runs and finishing 13th with a .410 slugging percentage despite a .258 batting average that was third behind Boston and Cleveland.
A three-time All-Star during a 19-year career that ended in 1999, Davis replaces Pat Roessler, who was fired after Mickey Callaway's first season as Mets manager.
New York also said Sunday it had hired Chuck Hernandez as bullpen coach and Luis Rojas for the new job of quality control coach.
Hernandez was fired after two seasons as Atlanta's pitching coach. He was pitching coach of the Angels (1992-96), Tampa Bay (2004-05) and Detroit (2006-08), and bullpen coach of Cleveland (2009).
Rojas is to be a conduit between the front office and coaching staff on game preparation, strategy and analytics.