Gvelesiani joined Persepolis in 2022 and contributed significantly to the team's success, helping secure two Iranian league titles, along with a Hazfi Cup and a Super Cup.
However, during the 2024-25 season, he struggled to meet expectations, leading to speculation about his departure once the season concludes.
Before joining Persepolis, the Georgia international defender played for the Iranian clubs Zob Ahan, Nassaji, and Sepahan.