In 1985 he graduated from the Faculty of Biology of the Tbilisi State University.
Zhvania entered national politics in 1988. In 1988-1990, his Green Party was one of a number of opposition groups that took part in Georgia's drive to regain its independence. In September 1991 his party joined the opposition to the government of the first post-Soviet President of Georgia, Zviad Gamsakhurdia. Gamsakhurdia's violent overthrow in January 1992 resulted in Eduard Shevardnadze, the former Soviet foreign minister, coming to power a few months later.
Shevardnadze established the Union of Citizens of Georgia to provide a moderate centre-right grouping for reformist democrats. Zhvania joined the UGC and recruited other reformists to the party, notably Mikhail Saakashvili. However, Zhvania fell out with Shevardnadze over a corruption scandal and resigned as speaker on November 1, 2001. He and Saakashvili also left Shevardnadze's party. He established a new party, called the United Democrats.
The parliamentary elections of November 2, 2003 were widely condemned by local and international observers as being grossly rigged by the government. In response, Zhvania and other opposition figures called for mass protests against Shevardnadze. Two weeks of massive popular protests followed, forcing Shevardnadze's resignation on November 23. He was replaced on an interim basis by Zhvania's successor as parliamentary speaker, Nino Burjanadze. Zhvania himself became a minister in the transitional government prior to fresh presidential elections held on January 4, 2004, which were won by Saakashvili.