Milei, who rode a wave of voter anger with the political mainstream, won by a wider-than-expected margin. He landed some 56% of the vote versus just over 44% for his rival, Peronist Economy Minister Sergio Massa, who conceded.
"The model of decadence has come to an end, there's no going back," Milei said in a defiant speech after the result, while also acknowledging the challenges that face him.
"We have monumental problems ahead: inflation, lack of work, and poverty," he said. "The situation is critical and there is no place for tepid half-measures."
In downtown Buenos Aires hundreds of Milei supporters honked horns and chanted his popular refrain against the political elite - "out with all of them" - as rock music played from speakers. Some people set off fireworks as excitement spread.
"We came to celebrate this historic triumph," said Efrain Viveros, a 21-year-old student from the province of Salta. "I'm honestly ecstatic. Milei represents change, for the better. With Massa we'd have had no future, our future has returned."
Milei is pledging economic shock therapy. His plans include shutting the central bank, ditching the peso, and slashing spending, potentially painful reforms that resonated with voters angry at the economic malaise.
His main platform has been to ditch the ailing peso for the US dollar and “dynamite” the Central Bank to do away with the “cancer of inflation.”
He is against abortion, pro-gun, vowed to cut ties with Argentina’s key trading partners China and Brazil, insulted Pope Francis, questioned the death toll under Argentina’s brutal dictatorship, and says humans are not behind climate change.