The Reds also optioned utility player Brandon Dixon to Triple-A Louisville and recalled Tanner Rainey and Cody Reed from Louisville to bolster a depleted bullpen.
The Dodgers sent James Marinan and Anerurys Zabala to the Reds for Floro, Zach Neal and international signing bonus pool space. Marinan will report to Billings of the rookie-level Pioneer League and Zabala to Class A Dayton.
Floro was 3-2 with a 2.72 earned-run average in 25 relief appearances this season with Cincinnati.
"He's got a good arm, a heavy sinker, puts the ball in the ground," Dodgers manager Dave Roberts said. "He's a guy that can go multiple innings if we need as well."
Rainey has no record in five previous stints with the Reds this season. Reed has spent the entire season with the Bats.
Dixon hit .219 with a home run and two runs batted in over 29 games, including 2-for-8 with two RBIs as a pinch-hitter.
To make room on the 40-man roster, the Dodgers designated right-hander Daniel Corcino for assignment.