New York traded minor league right-handers Miller Diaz and Matt Koch to Arizona in the deal, which was officially announced Sunday afternoon.
Reed, 26, is 2-2 with a 4.20 ERA in 38 appearances for Arizona this season. He is earning $4.875 million and remains under team control through 2017, but is a non-tender candidate because of the salary.
But with the suspension of Jenrry Mejia for performance-enhancing drugs and Bobby Parnell's struggles returning from Tommy John surgery, the Mets need other late-inning help -- particularly a reliever capable of handling lefty batters. The Mets have been depending heavily on rookies Hansel Robles and Logan Verrett in late innings during their playoff push.
Reed had cleared waivers earlier this month, making him eligible to be traded to any club.
He had a 5.92 ERA in his first 25 appearances of the season, but has performed better since a monthlong stint at Triple-A Reno. Since returning to the majors, Reed has a 1.65 ERA (3 ER in 16 1/3 IP) with 14 strikeouts, three walks and no homers allowed.
Reed resembles Clippard in that he can capably handle left-handed batters, which is a particular need for the Mets with recently acquired southpaw Eric O'Flaherty struggling and Jerry Blevins having refractured his left forearm. In his past three seasons, Reed has held lefty batters to averages .210, .219 and then .242 this season.
The Mets entered Sunday leading the Washington Nationals by 5½ games for first place in the National League East.