Mikitani tweeted a picture of himself boarding a private jet with Iniesta and the midfielder posted a photo of his own from inside the plane.
The 34-year-old ended his 22-year stay with the Spanish giants this season, having won 22 major titles.
He made 674 senior appearances, having joined the youth set-up aged 12.
The Spain international’s last game for Barcelona came in Sunday’s La Liga win over Real Sociedad, and Iniesta now looks set to join former Arsenal and Germany forward Lukas Podolski at Kobe.
The side are sixth in the J-League after 15 games, having finished ninth last season.
Iniesta, who scored the winning goal in the 2010 World Cup final against the Netherlands, has been selected for Spain’s squad for next month’s tournament in Russia.