Colon, 42, went 14-13 with a 4.16 ERA in 33 appearances (31 starts) for the Mets in 2015.
He reportedly will earn $7.25 million on the one-year deal.
With Jonathon Niese traded to the Pittsburgh Pirates for second baseman Neil Walker, the Mets were looking for a veteran rotation placeholder for Zack Wheeler, who is expected to return from Tommy John surgery in June or July. Matt Harvey, Jacob deGrom, Noah Syndergaard and Steven Matz make up the rest of the rotation.
Colon's 218 wins rank third among Dominican Republic-born pitchers, trailing only Juan Marichal (243) and Pedro Martinez (219).
Colon was praised for his clubhouse presence last season. He also proved adaptable and amenable to the bullpen. Colon pitched entirely in a relief role during the postseason.
Colon enjoyed a 31-inning scoreless streak late in the regular season. It marked the longest such streak in a single season by a pitcher 42 or older in major league history, according to the Elias Sports Bureau.
The Mets have now added Asdrubal Cabrera and Walker as middle infielders and re-signed left-handed reliever Jerry Blevins and Colon this offseason on major league contracts. With the retirement of Michael Cuddyer, team officials remain looking for a righty-hitting corner outfielder who potentially could fill in at first base, as well as a lefty-hitting complement to Juan Lagares in center field.