Polls by taken by TV stations shortly after voting closed indicated Mauricio Macri, 56, won, without giving a breakdown.
Mauricio Macri, the mayor of Buenos Aires, was up against Daniel Scioli, the governor of Buenos Aires province.
Loud cheers erupted at Mauricio Macri’s campaign headquarters at the news, Reuters reported.
Party insiders claimed a five- to eight-percentage-point lead.
If the result is confirmed, it will be the first time in more than a decade that Argentina’s center-right opposition has wrested the presidency from the center-left Peronists.
A spokesman for DanielScioli said they would wait for official figures to come in before commenting.
Neither candidate managed to win the first round of voting in October outright, forcing a runoff – the first in the country’s history.
DanielScioli was marginally ahead in the first round, with 36.7% to 34.5%, but has lost ground to his rival in the month since.
Mauricio Macri, the leader of the Cambiemos (Let’s Change) coalition, went into today’s vote with a comfortable lead in opinion polls.
He campaigned on pledges to bring new investment into the ailing economy, tackle crime and fight corruption.
The son of one of Argentina’s richest men, Mauricio Macri had a long career in business before entering politics.
A close ally of current President Cristina Fernandez de Kirchner, Daniel Scioli had been expected to win by a greater margin in October.
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