Nikkan Sports estimates the deal is worth approximately $3.5 million including signing bonus, base salary and performance bonuses.
The team is expected to make an official announcement after Jones passes a physical.
Jones, 35, batted just .197 with 14 home runs and 34 RBI in 94 games last season with the Yankees. He is a career .254 hitter with 434 home runs and 1,289 RBI in 2,196 games.
During his 17-year MLB career, Jones was a five-time All-Star and won 10 Gold Gloves. He broke in as a much-heralded rookie with the Braves in 1996 and played 12 years in Atlanta. He later played for the Dodgers, Rangers and White Sox.
Rakuten has been rumored to have interest in former major leaguer Manny Ramirez.