Heisey, who will turn 30 this month, is a .247 career hitter with 50 home runs over parts of five seasons with Cincinnati. He is eligible for salary arbitration and is projected to earn slightly more than $2 million in 2015.
The Reds dealt him several hours in advance of Tuesday night's MLB non-tender deadline. The Dodgers already had a glut of outfielders with Matt Kemp, Carl Crawford, Yasiel Puig, Andre Ethier and top prospect Joc Pederson, and the Heisey acquisition could be a precursor to more moves from Andrew Friedman, Los Angeles' new president of baseball operations.
Magill, 25, has an 0-2 record with a 6.51 ERA in six starts at the major league level, all in 2013. He posted a 7-6 mark with a 5.21 ERA in 12 starts (36 appearances) for Triple-A Albuquerque this past season.
"We are excited to be adding a player with a power arm who has a chance to help our club next season," Reds general manager Walt Jocketty said in a statement.