The clubs announced the deal Sunday.
Nuno never pitched for the Dodgers, who acquired him from Seattle in November in a trade for catcher Carlos Ruiz.
Nuno is 5-20 with a 4.02 ERA in 126 big league appearances with the Yankees, Diamondbacks and Mariners. He signed a $1.25 million, one-year deal in January.
The 22-year-old Moseley made a solid pro debut last season at Single-A Aberdeen. He was Baltimore's eighth-round pick from Texas Tech in 2016.
The Dodgers needed to clear a spot on their 40-man roster before announcing the signing of veteran outfielder Franklin Gutierrez, who was seen at their spring training complex in Arizona earlier Sunday.