TBILISI, Georgia — Salome Zurabishvili, the French-born former foreign minister of Georgia, claimed victory in a presidential runoff Wednesday that marked the final popular vote in the country for the head of state.

With nearly all of the ballots counted, the Central Election Commission said that Ms. Zurabishvili, 66, who was backed by the ruling Georgian Dream party, had won more than 59 percent of the vote in the race against Grigol Vashadze, 60, who was supported by a coalition of opposition forces.

Georgia, a nation of nearly 4 million people in the volatile Caucasus region south of Russia, is transitioning to a parliamentary republic that substantially reduces the authority of the president and elevates the prime minister to the most powerful figure in the country.

Once the term ends for Ms. Zurabishvili, the first woman to be elected president of Georgia, heads of state in the country will be chosen by delegates.