The Reds also placed right-hander Alfredo Simon on the 60-day disabled list, retroactive to Sept. 6. Simon is scheduled to undergo shoulder surgery on Tuesday.
Cincinnati claimed De Los Santos off waivers from Washington on July 19. He is a combined 2-3 with a 2.81 ERA and 11 saves in 46 games with Triple-A Syracuse and Double-A Harrisburg and Pensacola.
Magill is 4-1 with a 4.85 ERA and 38 saves for the Bats this season.