Greene, 18, pitched for Santa Monica High School in 2013.
The 170-pound righty has great downward plane on his fastball, something that could be a plus pitch as he fills out.
He also sports a curveball and splitter, although he'll need better command with all three of his pitches to have any success at the big league level.
That didn't stop him from dominating high school students in 2013, as Greene had a 1.68 ERA with 76 strikeouts in 50 innings.
"This year, the pressure was on me to perform, and I usually thrive under pressure," Greene said to the Santa Monica Mirror prior to being drafted. "I think, overall, it turned out well, because as a pitcher, you try to repeat your motion over and over, and I felt like I did that throughout the season."
Greene will play for College of Southern Nevada if he doesn't sign with the Blue Jays, but turning professional seems more likely.
"Being a professional ballplayer has always been my dream, but making a 40-man roster is the ultimate goal," said Greene. "Hopefully, I'm given a fair enough offer where I can finally achieve my dream and go out there and play baseball."
Evan Peaslee is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.