Dvalishvili was signed by
Olimpi Rustavi in June 2006. On 7 July 2009, Dvalishvili signed a two-year contract with the Israeli champions
Maccabi Haifa. Dvalishvili made his debut on
2009–10 UEFA Champions League Second qualifying round, 15 July 2009, against
Glentoran and scored two goals. In the next round, against
Aktobe, Dvalishvili scored the last two goals in Maccabi Haifa's great comeback – scoring four straight goals after falling down 3–0 in the first 15 minutes of the match. In January 2012, Dvalishvili joined Polish club
Polonia Warsaw in the
Ekstraklasa on a two-and-a-half-year contract. Dvalishvili joined
Legia Warsaw on 15 February 2013 on a two-and-a-half-year contract. The club finished the 2012–13 season with the
double (cup and championship). On 12 August 2014, "Lado" left Legia under mutual agreement and, a day later, he signed a two-year contract with
Odense BK. On 27 August 2015 29-year-old Dvalishvili signed 3-year contract with
Pogon. In July 2016 Dvalishvili returned to Georgia, after agreeing to a half-year contract with
FC Dinamo Tbilisi. ==International career==