Easley, a 15-year major league veteran, played last season with the Arizona Diamondbacks, batting .233 (44-189) with nine home runs and 28 RBI in 90 games.
"Damion is a versatile guy who can play all over the field," Mets general manager Omar Minaya said. "He provides us with power coming off the bench, too. Damion Easley is the type of player who can help your club win games in so many different ways."
Signing Easley is the fourth transaction that Minaya accomplished this week during the GM meetings in Naples, Fla.
Earlier, the Mets re-signed free agents Orlando Hernandez and Jose Valentin, and on Wednesday the Mets acquired outfielder Ben Johnson and pitcher Jon Adkins from the San Diego Padres for pitchers Heath Bell and Royce Ring.
Standridge, 28, appeared in 21 games for the Reds in 2006, going 1-1 with a 4.82 ERA. He is likely get a look in spring training as a candidate for the bullpen but could run into tight competition.