Ex-diplomat Salome Zurabishvili hailed her election as Georgia's first woman president on Thursday but opposition leaders denounced the result as fraud and called for protests.
With all votes counted, the country's election commission said the French-born Zurabishvili, backed by the ruling Georgian Dream party, had taken 59.52 percent of the second-round vote.
Her rival Grigol Vashadze, from an alliance of 11 opposition parties led by exiled ex-president Mikheil Saakashvili's United National Movement (UNM), took 40.48 percent.
Zurabishvili said her election was a step forward for women and a move closer to Europe for the ex-Soviet republic.
"It is now important to show that this country has chosen Europe," she told journalists after her win. "For that purpose, Georgians have elected a European woman president."
"It feels great," she said, pointing out that she was one of a small number of women presidents in the world.
But opposition leaders -- who have accused authorities of vote-buying and ballot stuffing -- refused to accept the result.
"We do not recognise the election results, we demand the holding of snap parliamentary polls," Vashadze said in televised remarks, calling for "a mass peaceful demonstration" in the capital Tbilisi on Sunday.
The election was seen as a test of Georgia's democratic credentials as it seeks European Union and NATO membership.
It was also a trial run for more important parliamentary elections in 2020, when Georgian Dream is set to face off against a range of opposition parties.
The party is the creation of billionaire tycoon Bidzina Ivanishvili, who many see as the small country's de facto ruler.
Flamboyant ex-president Saakashvili, who lives in exile in the Netherlands, claimed "mass electoral fraud" even before official results were released.
"The oligarch has stamped out Georgian democracy and the institutions of elections," he said on the pro-opposition Rustavi-2 television channel, referring to Ivanishvili.
"I urge Georgians to defend our freedom, democracy and the law. I call on you to start mass peaceful rallies and demand snap parliamentary polls."
International observers said there were problems with the election but that overall it had been "competitive".
"(The) election was competitive and candidates were able to campaign freely, however one side enjoyed an undue advantage," monitors from the Organisation for Security and Cooperation in Europe said in a report after the vote.
The elections were "well administered", they said, but raised concerns about misuse of administrative resources that "blurred the line between party and state".
Tensions increased ahead of the second round, as the opposition accused the government of voter intimidation and claimed that ruling party activists had attacked Vashadze campaign staff.
Zurabishvili in turn said she and her children had received death threats through text and voice messages from people affiliated with the UNM.
Vashadze, a 60-year-old career diplomat, had criticised Ivanishvili's "informal oligarch rule" amid growing discontent over the government's failure to tackle poverty.
The vote was Georgia's last direct leadership poll as it transitions to a parliamentary form of governance. The first round of the presidential election on October 28 saw Zurabishvili take 39 percent of the vote, against 38 percent for Vashadze.
Street protests against the results could spark concern for the country, which has seen civil wars, mass demonstrations and unrest since gaining its independence in 1991 with the breakup of the Soviet Union.
A smooth presidential transition, however, would be welcomed by many as a sign of stability in Georgia, which is emerging as a tourism hotspot and hopes for more foreign investment.
Daughter Of Refugees
Zurabishvili, a 66-year-old independent lawmaker, is the daughter of refugees who fled Georgia in 1921 for Paris after the country's annexation by the Red Army.
Her career in France's foreign service culminated in a posting to Tbilisi, where then-president Saakashvili appointed her foreign minister.
But Zurabishvili quickly made enemies among the parliamentary majority, with MPs and some senior diplomats accusing her of arrogance and impulsiveness.
When she was sacked after a year in the job, thousands took to the streets of the capital to protest her dismissal.
On Thursday morning she received blessings from the influential head of Georgia's Orthodox Church, Catholicos-Patriarch Ilia II, and was later seen by passersby sipping coffee with her children on a sunny terrace in central Tbilisi.
The French foreign ministry said in a statement that Paris was looking forward to working with Zurabishvili "to further strengthen" relations.