[8] As with many leading Georgian players, Kavelashvili began his career with Dinamo Tbilisi, emerging from their youth system in 1989.

Kavelashvili joined Basel's first team during their 2005–06 season under head coach Christian Gross, who was behind Grasshoppers' league win in 1998.

Kavelashvili played his domestic league debut for the club in the home game in the St. Jakob-Park on 12 March 2006 as he was substituted in the 66th minute; he scored the only goal of the win over Grasshoppers.

[13] Basel had started the season well and were joint leaders of the championship with Zürich right until the last day of the league campaign, when they lost the title on goal difference.

In his second season, he made seven appearances, again each as substitute, but the club released him before the winter break, and he retired from his active football career.

[16] In 2015, he planned to run for president of the Georgian Football Federation, but due to a lack of higher education, he was unable to participate in the election.

[18] He also accused the West of wanting "as many people as possible (to be) neutral and tolerant towards the LGBTQ ideology", which he called "an act against humanity".

[23] As the sole candidate Kavelashvili received 224 out of 225 votes of the 300-member electoral college and was proclaimed the next president,[24] with a scheduled inauguration on 29 December 2024.

Salome Zourabichvili, along with opposition parties and the majority of civil society, continued to assert her recognition as the legitimate President of Georgia.