According to the poll conducted by Gallup International for Imedi television, Zurabishvili, 66, wins 58 percent of the ballots.
Meanwhile, a poll conducted by Edison Research for Rustavi-2 television indicates that Zurabishvili wins 55 percent of the votes, giving opposition candidate Grigol Vashadze 45 percent of ballots.
Vashadze, 60, has already dismissed the results of exit polls and refused to acknowledge defeat until final results of the vote are announced. He is backed by Mikheil Saakashvili, Georgia's former president who lives in exile.
In an interview with Rustavi-2, Saakashvili said the runoff was illegitimate and called for peaceful protest to demand snap parliamentary elections.
'This was not a legitimate election. We do not recognize its outcome, which has nothing to do with democracy. I call on the Georgian public to start demanding early parliamentary elections and to reject the presidential voting result through peaceful rallies', he said.
The ex-president again promised to return to Georgia, where he is wanted on criminal charges. He says they are politically motivated. Vashadze has vowed to pardon Saakashvili and others Georgian dignitaries on the wanted list if he were elected.
The second round of presidential elections was held in Georgia on Wednesday as candidates had failed to gain required 50 percent of votes during the first vote.
This presidential election in Georgia is the last direct vote to elect the country's leader by people. All following presidents will be chosen by a special panel consisting of 300 electors. Given these changes, the president who will be elected this year will spend six years in the office instead of five.