He started his career as a scrum-half but now plays as a fly-half and occasional fullback and is the all-time leading points scorer for the Georgia national rugby union team.

He left Georgia in 2006 for Pro D2 side Pau, and has since moved on to three other French clubs in Fédérale 1 in Massy, Figeac and most recently Saint-Junien where he joined after the 2011 World Cup and currently plays.

However he failed to establish himself in the Georgian side over the next couple of years, with Irakli Abuseridze and Bidzina Samkharadze both ahead of him for selection in the scrum half position.

After Malaghuradze suffered an injury and then a loss of form, Kvirikashvili returned to the first choice fly half position in 2011 helping Georgia to an undefeated season in the European Nations Cup.

In July 2016, Kvirikashvili was involved in a car accident on the Kutaisi-Samtredia highway, while travelling with fellow rugby player Giorgi Lominadze and their respective wives.