Exit polls broadcast by several television channels including TN, C5N and Canal 26 just after voting closed at 2100 GMT indicated Macri, 56, had won the vote, without giving a breakdown.
Official results were due in the coming hours, but cheering, dancing crowds of Macri's supporters were already celebrating at his post-election rally in a conference center on the outskirts of Buenos Aires.
His rival Daniel Scioli's camp, gathered in a city center hotel, had yet to react.
That result forced Argentina's first ever presidential runoff.
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If yesterday's result is confirmed, Macri will become the most economically liberal president since the 1990s at the helm of Latin America's third-biggest economy.
He has capitalized on discontent among voters who said they were fed up after 12 years of rule by Kirchner and her predecessor and late husband, Nestor Kirchner.
With social welfare programs and protectionist economic policies, they won affection among poorer Argentines and mistrust among foreign investors.
Macri has vowed to free up trade, liberalize the economy and negotiate with Argentina's foreign debtors.