Meshvildishvili, representing Georgia, won the European Sumo Championship. In 2015 European U23 Wrestling Championships, he won a silver medal at the European U23 Wrestling Championships in Poland, losing in the final to Muradin Kushkhov of Russia. In 2021, Meshvildishvili won the Azerbaijani Open Championship. He also won international tournaments in Kyiv, Vladikavkaz, Poland, Armenia and Kazakhstan. The way of the athlete to the world and European championships in freestyle wrestling was often blocked by the leader of the Georgian team, two-time Olympic medalist Geno Petriashvili.[4]
Meshvildishvili made his debut as a member of the Azerbaijani team in early February at a ranking tournament in Croatia. At this tournament in Zagreb, Meshvildishvili reached the final, where he was to fight with Amir Husein Abbas of Iran, but didn't appear on the mat because of an injury. As a result, Meshvildishvili suffered a technical defeat and settled for the silver medal.[5]
In April 2023 he took part in the 2023 European Wrestling Championships in Zagreb. Meshvildishvili defeated Gennady Chudinovich of Germany in qualification, but lost in the quarterfinals to Taha Akgul of Turkey. In the bronze medal he defeated Abraham Conyedo of Italy.[6][7]
He competed at the 2024 European Wrestling Olympic Qualification Tournament in Baku, Azerbaijan and he earned a quota place for Azerbaijan for the 2024 Summer Olympics in Paris, France.[8] He won one of the bronze medals in the men's freestyle 125 kg event at the Olympics.[3]
As of April 1, 2026, with a score of 460 points, holds second place in the ranking of Azerbaijani athletes according to the Ministry of Youth and Sports.[9]
On April 25, 2026, at the European Wrestling Championship in Tirana, he defeated Turkish athlete Hakan Büyükçıngıl with a score of 3:1 and advanced to the final, where he overcame Vladislav Baytsaev (Hungary) and won the gold medal.[10]