Ona is the No. 8 international prospect of the 2016 class, according to MLBPipeline.com. The righty slugger hit .319 for Cuba's 18U National League team in 2014 and starred at the 2014 COPABE 18U Pan American Championship in Mexico.
Padres general manager A.J. Preller said Ona will report to the instructional league to work with San Diego's other recent international signees, and he will begin his pro career in 2017.
Preller called Ona an advanced hitter with a body reminiscent of Albert Belle.
"The guy's got a compact swing with strength," Preller said. "He's got a really good bat path, good bat-ball skills."
Including Ona, the Padres have now signed 28 international prospects since the international signing period began on July 2, and that list includes Cuban left-hander Adrian Morejon, ranked No. 2, for $11 million. The club also signed shortstop Luis Almanzar, ranked No. 4, to a $4 million deal; shortstop Gabriel Arias, ranked No. 6, for $1.9 million; outfielder Jeisson Rosario, ranked No. 12, for $1.85 million; shortstop Jordy Barley, ranked No. 18, for $1 million; and shortstop Justin Lopez, ranked No. 30, for $1.2 million.
The Padres are already facing the most severe penalty for exceeding their pool by 15 percent or more, so they will not be allowed to sign a player for more than $300,000 during the next two signing periods. They must pay a 100 percent tax on the pool overage, a total close to $58 million, in addition to the estimated $32 million spent on prospect bonuses.
Ona's deal is pending a physical.
Preller said many teams seem to be interested in starting pitcher Andrew Cashner, but San Diego will only deal him if the right offer comes along.
"He's a quality Major League starting pitcher," Preller said. "We're going to listen, as we would with any player, but for us to make a deal, it'll have to be something that really intrigued us."