The 34-year-old playmaker left Barcelona at the end of the Spanish season and has since been strongly linked with the J1 League club.
Iniesta wrote on Instagram on Wednesday: “Heading to my new home, with my friend @hiroshi.mikitani”
In the accompanying picture, Iniesta is shown on an aeroplane locking hands with Mikitani, who owns Vissel Kobe and is the founder and chief executive of e-commerce giant Rakuten.