The two men held talks for more than an hour at the Vatican before Milei met with the pope's top aides, with discussions including the economic crisis in Argentina, the Holy See said.
While campaigning for election last year, Milei had sharply criticised the pontiff, accusing him of political interference and calling him an "imbecile" who "promotes communism".
But in an interview this weekend he described Francis, a former archbishop of Buenos Aires, as "the most important Argentine in history".
A video of Monday's meeting released by the Vatican showed the two men smiling and joking, and the president gave Francis gifts including Argentine biscuits that he is said to enjoy, officials said.
Milei also gave the pope a big hug when they met briefly at St Peter's Basilica on Sunday, on the occasion of a papal mass for Argentina's first female saint.
Francis had brushed off Milei's earlier criticism as rhetoric in the heat of a campaign, and called the newly elected president in November to congratulate him on his win.
The president asked Francis to visit Argentina, a trip the 87-year-old pope has said he would like to make.
But no date has yet been set for the visit, which would be his first since becoming head of the Catholic Church in 2013.
Milei also met Monday with Italy's President Sergio Mattarella and with Prime Minister Giorgia Meloni.
- Economic crisis -
Milei and Pope Francis were both born in Buenos Aires but have different views of the world.
One is a liberal economist and climate change sceptic on a drive to deregulate Argentina's economy, the other a champion of the poor who regularly attacks the power of financial markets and blames humankind for global warming.
After their talks, Milei met with Vatican Secretary of State Pietro Parolin and de facto foreign minister Paul Richard Gallagher.
Among the topics of discussion, Milei and Francis "addressed the new government's programme to counter the economic crisis," the Vatican said in a statement.
Some 40 percent of Argentines are living in poverty, while crippling inflation tops 200 percent.
Elected on a wave of anger over decades of economic crisis, Milei has embarked on massive economic deregulation by presidential decree.
He has devalued the peso, cut state subsidies and scrapped hundreds of rules.
His reform package hit a roadblock last week, however, when parliament sent it back to committee for a rewrite, prompting Milei to lash out at his opponents, calling them "criminals" and "traitors".
In January, Milei sent the pope a letter, saying a visit would "result in peacemaking and brotherhood for all Argentines, eager to overcome divisions and confrontations".
- Suffering men and women -
Throughout his papacy, Francis has railed against the inequalities generated by free markets, calling for the protection of society's most vulnerable.
During Sunday's mass, at which the 18th-century missionary Mama Antula was canonised, Francis again made a plea on behalf of society's most marginalised.
"How many suffering men and women do we meet on the sidewalks of our cities," he lamented during his address.
Mama Antula, a consecrated Jesuit laywoman born Maria Antonia de Paz y Figueroa, is considered a champion of human rights from the period when Argentina was a Spanish colony.
Milei had arrived in Rome from an official visit to Israel, where he made waves by likening Hamas's attacks on Israel to the Holocaust and announced plans to move the Argentinian embassy to Jerusalem.
Although from a Catholic family, he has expressed his fascination with Judaism and has been studying the Torah.
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