Gegeshidze represented Georgia at the 2012 Summer Olympics in London, where he competed in the men's 84 kg class. He defeated Azerbaijan's Saman Tahmasebi and Ukraine's Vasyl Rachyba in the preliminary rounds, before losing out the semi-final match to Russia's Alan Khugayev, who was able to score three points each in two straight periods, leaving Gegeshidze with a single point. Because Khugayev advanced further into the final round against Egyptian wrestler and former Olympic champion Karam Gaber, Gegeshidze automatically qualified for the bronze medal match, where he was defeated by Kazakhstan's Daniyal Gadzhiyev, with a three-set technical score (1–0, 0–1, 0–2), and a classification point score of 1–3.