Green spent the last of his five seasons with the Utes as the team's go-to closer. Six of Green's eight career saves came this season, when he posted a 4.26 ERA in 23 appearances. He held opponents to a .256 batting average, and struck out 38 compared to 12 walks.
"Our cross-checker told me, 'Look, you have to take this guy, he's got a plus slider,'" Royals director of scouting Lonnie Goldberg said.
All 70 of Green's career appearances came in relief.
The Draft concludes on Saturday, with exclusive coverage of Rounds 11-40 beginning on MLB.com at noon CT.
Jackson Alexander is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.