Gutierrez and right-handed pitcher Yadier Alvarez, 19, ranked No. 2 on MLB.com's Top 30 International Prospects list, are considered the two best young Cuban pitchers to become available this year. Alvarez signed a $16 million deal with the Dodgers on Thursday.
Outfielder Eddy Julio Martinez, ranked No. 1, is also from Cuba and is expected to command a bonus in excess of $10 million.
It's unclear what the market for Gutierrez will be, but it will likely be determined after he begins working out for teams next month.
Gutierrez left his Pinar del Rio team during the Caribbean Series in February in San Juan, Puerto Rico, and made his way to Mexico, where he eventually established residency in May.
The 6-foot-3, 172-pound right-hander was the Serie Nacional Rookie of the Year during the 2013-14 season. He went 5-5 with a 3.90 ERA during his rookie season, primarily pitching out of the bullpen. He also sported a 2.45 ERA as a reliever during the current 2014-15 season.
Gutierrez is subject to the international signing guidelines because he is under 23 and played less than five years in the Serie Nacional.
Jesse Sanchez is a national reporter for MLB.com. Follow him on Twitter @JesseSanchezMLB. This story was not subject to the approval of Major League Baseball or its clubs.