Although she sits in parliament as an independent , Zurabishvili is the ruling Georgian Dream party's candidate for president.
Her principal rival, Grigol Vashadze, is also a former diplomat, starting his career in the Soviet Union, and is backed by the opposition National Movement.
The post of president will become largely ceremonial after the election, due to a constitutional reform agreed last year, but the election has been hard fought and largely based on opposing views of the record of Georgian Dream in power.
Born in Paris
Zurabisvili was born in Paris in 1952, her parents having fled the Soviet Union in 1921 during the wars and turmoil that followed the 1917 Russian revolution.
After attending university in France and the US and a successful career at the French foreign affairs ministry, she was appointed ambassador to Georgia, by now an independent republic, by then president Jacques Chirac in 2003.
The month after her arrival the Rose Revolution erupted, driving Edvard Shevardnadze out of power, to be replaced by Mikhail Saakashvili.
The new president named Zurabishvili foreign affairs minister in 2004, only to fire her after a year, despite large demonstrations in her support.
She then became a vocal critic of her former boss, founding a party called Georgia's Way that became part of the United Opposition alliance.
In 2010 she quit Georgia's Way, sitting in parliament as an independent.
Backed by billionaire
Her presidential bid is backed by Georgian Dream and by former prime minister Bidzina Ivanishvili, a billionaire who is credited with decisive influence over the ruling party.
Both Zurabishvili and Vashadze support closer ties with the European Union and the Nato military alliance, which the country has been trying to join for more than 10 years, a proposal that is bitterly opposed by Vladimir Putin's Russia.
Vashadze accuses Georgian Dream of failing to tackle poverty and extensive corruption.
Sunday's vote is probably the last time Georgia's president will be directly elected.
The new constitution means that the post will be filled by a vote of a 300-member electoral college from 2024 onwards.
The changes did not go as far as a 2008 proposal by Georgian Orthodox Church Patriarch Ilia, backed by Zurabishvili along with several other politicians, to restore the monarchy.