Born in Batumi, Chogadze is a product of a youth sportive system of the Saburtalo Tbilisi, where he signed his first professional contract. After playing in the different Erovnuli Liga teams, in January 2020 he was transferred to Ukraine and signed a 1,5 year deal with Olimpik Donetsk.[1]
Chogadze made his debut in the Ukrainian Premier League for FC Olimpik as a start-squad player on 23 February 2020, playing in a losing home match against FC Lviv.[2] In 2022, he moved to Kazakhstan to play for Shakhter. Following a brief tenure at Nasaf in Uzbekistan, in the summer of 2024 Chogadze returned to KPL and signed for Zhetysu.[3]