Sometimes dubbed "El Loco" (the madman) by his critics, Mr Milei has promised drastic changes, which include ditching the local currency, the peso, for the US dollar and "blowing up" the central bank in order to prevent it from printing more money, which he argues is driving inflation.
He has also proposed cutting welfare payments and slashing bureaucracy by closing the ministries of culture, women, health and education, among others.
On social issues, the president-elect wants to loosen gun laws, abolish abortion - which was legalised in Argentina in 2020 - and allow the sale and purchase of human organs.
He also announced that the changes he would bring in would be drastic and immediate.
During campaigning, the former economist and pundit held a chainsaw aloft to symbolise plans to cut spending.
Mr Milei's victory comes amid a deep economic crisis which has seen annual inflation rise to 143% and 40% of Argentines living in poverty.
The president-elect's aggressive style and promises to challenge the political establishment resonated with voters fed up with traditional parties.
In his victory speech, Milei pledged immediate and drastic changes, positioning Argentina for a new era. Economists, however, caution that Milei, whose party holds a small number of seats in Congress, will need to negotiate with established politicians.
However, economists have been more circumspect, pointing out that Mr Milei's party only holds a small number of seats in Argentina's Congress and that he will therefore have to negotiate with the very politicians he disparaged and attacked during the campaign.
His choice of Victoria Villarruel as his vice-presidential running mate shocked human rights campaigners in the country, in which 30,000 people were killed or forcibly disappeared under military rule from 1976 to 1983.
Ms Villarruel, who comes from a military family, has defended officers convicted of crimes against humanity and proposed dismantling a museum which commemorates victims of Argentina's military junta.
Mr Milei and Ms Villarruel will be sworn in on 10 December for a four-year term.