Gorgodze switched to rugby from basketball aged 17. His first club was Lelo in the Georgian Top League, he was soon selected for the Georgia national team and made his debut in 2003 against Spain, at the age of just 18 and not long after he started playing rugby. However he wasn't selected for Georgia's first appearance at the 2003 Rugby World Cup later that year. In 2004 he became a regular fixture for the Georgia side.
Montpellier
Gorgodze signed for Montpellier in 2005. Gorgodze started his career at Montpellier mainly as a reserve in the side and didn't get much game time. He was still a regular in the Georgia side though and was selected for the 2007 Rugby World Cup. Gorgodze started three of Georgia's four matches at the World Cup, and was one of Georgia's star players. After the 2007 Rugby World Cup, Gorgodze started playing for Montpellier a lot more regularly and was their first choice lock. Gorgodze was signed by Brive for the 2009/10 season but Gorgodze changed his mind and decided to stay at Montpellier, who were forced to pay Brive 200,000 euros to keep him. A known weak spot for Gorgodze is his indiscipline, he has received 16 yellow cards for Montpellier since 2007. During 2010 he was banned twice for fighting, once with Sébastien Pagès against Albi and the other time with Alex Tulou against Bourgoin. Gorgodze changed position for Georgia to the back row, and when Fabien Galthié and Eric Béchu became the new Montpellier coaches before the 2010/11 season they also converted him to the back row. Gorgodze became a revelation at flanker during this season, and halfway through the season French newspaper L'Équipe commented that he improved his technique and became a mobile and unstoppable player. Gorgodze played a big role in Montpellier finishing the 2010/11 Top 14 as runners up, and had a particularly massive match in the Top 14 semi final against Racing-Métro. At the end of the season L'Équipe named him as the best foreigner in the league. Gorgodze was selected for the Georgia squad for the 2011 Rugby World Cup and played all the Georgia matches and was named man of the match in two matches, against England and Romania. Gorgodze had signed a preliminary contract with Toulon in advance of the 2011–12 season, but changed his mind and signed an extension to his deal with Montpellier. This led to a tribunal hearing, but an amicable settlement was soon reached.
Toulon
In November 2013, as his contract with Montpellier was expiring, he signed a three-year deal with Toulon to take effect with the 2014–15 season. His competitive debut with Toulon was delayed due to a knee injury during a preseason friendly with Racing Métro; he is expected to miss the first two to three weeks of the 2014–15 season.
