Blevins, 31, spent the first seven seasons of his career in the Oakland Athletics' bullpen before going to Washington in 2014.
Last season, Blevins appeared in 64 games for Washington, amassing a 2-3 record and a 4.87 ERA.
Den Dekker, a fifth-round pick by the Mets in 2010, will bring outfield depth to the Nationals. In 237 career Major League plate appearances he's hit one home run and posted a .238 career batting average.
New York will take on Blevins' entire salary in 2015, Fox Sports reported. He is due $2.4 million this upcoming season.
- Will Green