Rigi penned a two-year contract with Sepahan for an undisclosed fee.
He joined Esteghlal from Padideh in 2019 and played in the first team over the past two years.
He had also been linked with a move to Emirati and Qatari teams.
The 30-year-old defensive midfielder started his playing career in 2011 in Fajr Sepasi.