In return for Reed, the Mets will acquire three prospects from the Red Sox: right-hander Jamie Callahan, right-hander Stephen Nogosek and right-hander Gerson Bautista, a source confirmed to ESPN's Keith Law.
The New York Post first reported the trade.
Reed, 28, is 1-2 with a 2.57 ERA in 48 appearances this season. He has been the Mets' closer in Jeurys Familia's absence and has 19 saves this season. Reed would be expected to return to a setup role behind Craig Kimbrel.
The Mets acquired Reed in August 2015. He was part of the team's first trip to the World Series since 2000 but was the losing pitcher in New York's decisive Game 5 defeat to the Kansas City Royals.
Reed will be a free agent after the season.
The Mets' loss of Reed is softened by their acquisition of proven closer AJ Ramos in a trade with the Miami Marlins over the weekend.
Callahan, 23, is 5-2 with a 3.21 ERA and six saves in two stops in the Red Sox's system. He is currently pitching at Triple-A Pawtucket. Nogosek, a 22-year-old reliever, is 4-4 with a 3.06 ERA and 19 saves in two stops in Boston's system. He is currently at Salem, the Red Sox's advanced Class A affiliate in the Carolina League. Bautista, a 23-year-old reliever who also is at Salem, has a 3-2 record, a 5.16 ERA and four saves.