KORYO, Japan—The dream Shota Tatsuta shared with his grade-school classmates nearly 10 years ago of becoming a professional baseball player is a dream no longer. On Thursday, the high-school pitcher was picked in Japan’s baseball draft by the Nippon-Ham Fighters.

It’s a sweet conclusion to the 18-year-old Shota’s youth baseball career. While he had led two teams to national championships and pitched for the Japan national youth team at a world tournament, he had failed to make it to the famous summer Koshien national high-school...