The center-left candidate was handpicked by two-term President Cristina Fernandez de Kirchner, who is constitutionally barred from seeking a third term.
The head of the campaign led by Daniel Scioli’s main challenger, center-right Buenos Aires Mayor Mauricio Macri, says the election is heading for a second round.
A run-off would be held on November 22.
Argentina’s C5N television network said Daniel Scioli had won by “a large margin”.
To win outright, a candidate needs 45% of the vote or a minimum of 40% as well as a 10-point lead over the nearest rival.
Daniel Scioli, the governor of Buenos Aires province, is a former world power boating champion who lost his right arm in a race in 1989.
Last week, he pledged tax cuts for workers earning under a certain income, a move expected to affect half a million people.
Daniel Scioli has also vowed to bring down Argentina’s inflation to single digits in less than four years and promises to introduce policy changes to invigorate the economy.
Another candidate, Sergio Massa, a former ally of Cristina Fernandez de Kirchner, is polling behind Mauricio Macri. There are three other names on the ballot paper, with 32 million people eligible to vote.
Long queues formed outside polling stations from the early hours on October 25.
Cristina Fernandez de Kirchner, who stands down after eight years in power, says she leaves Argentines a better country.
“We are voting today in a completely normal country,” she said after casting her vote in the Patagonian town of Rio Gallegos.
In previous decades, Argentines always went to the polls “in the middle of a serious crisis,” Cristina Fernandez de Kirchner added.
She said achieving stability and leaving Argentines “a normal country” was the promise made by her late husband, Neston Kirchner, when he took office in 2003.
Nestor Kirchner died in 2010, three years after handing over the presidency to his wife.
Whoever wins Argentina’s presidency faces significant economic challenges.
While Argentina gained strength after a financial crisis in 2002, its economy, the third-largest in Latin America, has slowed in recent years, with GDP growing by only 0.5% in 2014.
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