The 28-year-old player has penned a two-year contract for an undisclosed fee with the Isfahan-based football club.
The 28-year-old defender is going to replace Siavash Yazdani, who has been reportedly linked with a move to Esteghlal.
Gvelesiani started his playing career in Iran at Zob Ahan in 2017 and was a member of Nassaji in the last season.
Sepahan is strengthening itself for the Iran Professional League new season and 2020 AFC Champions League.