Greene, 17, is the only player picked in the top 10 to remain unsigned. Selected out of Notre Dame High School in Sherman Oaks, Calif., he was ranked as the No. 1 prospect in the Draft by MLBPipeline.com.
Scouting reports have shown that Greene is able to throw 102 mph, and he has the potential to be a dynamic Major Leaguer.
Cincinnati has signed 22 of its 41 picks this year, with Greene the only one unsigned among the organization's first 11 selections. On Tuesday the Reds signed their seventh-round pick, catcher Mark Kolozsvary from the University of Florida.