The 28-year-old player is a member of Dinamo Tbilisi from 2010.
Zob Ahan’s newly-appointed coach Amir Ghalenoei traveled to Georgia last month to see Gvelesiani’s performance.
According to Iranian media, Gvelesiani has already played for Georgia national football team.
Last season, Zob Ahan finished in fourth place, 20 points adrift of Iran Professional League leader Persepolis.
Former Esteghlal and Tractor Sazi coach Ghalenoei replaced Mojtaba Hosseini last month.