Kvilitaia was born in Abasha, Georgia. At age 14 he moved to Tbilisi, first to Norchi Dinamo and later to Division 2 side Sasco, where he was one of the best scorers in 2012–13.[1]
After an unsuccessful spell at Győr, Kvilitaia played one season for Dila Gori on loan. In June 2015 he joined Dinamo Tbilisi.[2]
With 24 goals scored in 29 matches this season, Kvilitaia became a top scorer and won the special prize at a GFF award ceremony.[3]
After two seasons he signed a four-year deal with Belgian side Gent.[5]
Since 2020 Kvilitaia has been playing in the Cypriot First Division. Initially, on 17 September 2020 he joined Anorthosis[6] on loan from Gent and a year later he moved to APOEL on 3 June 2021.[7] In August 2021, he was selected as a team captain.[8] In May 2024, Kvilitaia became the winner of the league season with this club and shortly joined Aris Limassol on a three-year deal.
[9]