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 2009-2010 Union of European Football Associations 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 2012-2013 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.
He made his Georgia debut on 6 June 2009.
On 9 September 2009 Dvalishvili scored a goal in a friendly match his country lost 2–1 to Iceland.