Reed, 25, was designated for assignment and removed from the Dodgers' 40-man roster last week.
In exchange for Reed, the Dodgers received Grant Dayton from the Marlins.
Dayton, 27, was 2-1 with a 2.83 ERA (11 ER/35.0 IP) and 35 strikeouts in 25 games for Triple-A New Orleans this season. Left-handers were hitting .182 against him.
Dayton will report to Triple-A Oklahoma City.
Reed was drafted out of Stanford by the Dodgers in 2011. In 24 games at double-A Tulsa and triple-A Oklahoma City this season, he had a 5.97 earned-run average. He entered this season ranked by Baseball America as the 10th-best prospect in the Dodgers system.