Reed was designated for assignment on Friday when the club claimed relief pitcher Preston Guilmet off waivers from the Rays, after Reed struggled most of the season after switching from starting to relief.
Dayton, 27, was 2-1 with a 2.83 ERA in 25 games for Triple-A New Orleans this season, with 35 strikeouts and five walks in 35 innings. In 64 games in Triple-A over the last two seasons, Dayton has a 27-percent strikeout rate and 7.3-percent walk rate.
Left-handed batters this season are just 6-for-33 (.182) with a double against Dayton this season, with 11 strikeouts and one walk.
He was drafted by the Marlins in the 11th round in 2010 out of Auburn.
Dayton is not on the 40-man roster. He was designated for assignment by the Marlins on April 24, then sent outright to Triple-A two days later. He has used options in 2014 and 2015, and has no major league service time.
The Dodgers assigned Dayton to Triple-A Oklahoma City. He last pitched for New Orleans on Friday.
In another minor league transaction on Wednesday, the Dodgers released left-handed pitcher Jeremy Horst. The 29-year-old southpaw had a 1.64 ERA in 32 relief appearances for Double-A Tulsa, with 42 strikeouts and 20 walks in 38⅓ innings.