Ms Meloni, 45, whose political party has neo-fascist roots, took the oath of office before the Italian president at the presidential palace.
Her Brothers of Italy party won the largest vote in last month’s national election.
“I swear to be faithful to the republic,” the 45-year-old Ms Meloni said, reciting the ritual oath of office under the crystal chandeliers of the chamber before shaking hands with President Sergio Mattarella.
The pledge was signed by her and counter-signed by Mr Mattarella, who serves as guarantor of the Constitution, drafted in the years immediately after the end of war, which saw the demise of fascist dictator Benito Mussolini.
Ms Meloni’s 24 ministers followed, similarly swearing in. Five of the ministers are technocrats, not representing any party. Six of them are women.
Ms Meloni will head her first Cabinet meeting on Sunday. Her government replaces that led by Mario Draghi, a former European Central Bank chief, who was appointed by Mr Mattarella in 2021 to lead a pandemic national unity coalition.
Ms Meloni was the sole major party leader to refuse to join the coalition, insisting the nation’s voters return to the polls, which they did on September 25.
European Commission chief Ursula von der Leyen congratulated Ms Meloni on Saturday and said she looked forward to “constructive co-operation” with her government.
“Congratulations to Giorgia Meloni on her appointment as Italian Prime Minister, the first woman to hold the post,” Ms von der Leyen wrote on Twitter.
“I count on and look forward to constructive co-operation with the new government on the challenges we face together.”
Ms Meloni announced her Cabinet on Friday evening when she accepted a mandate to form Italy's next government.
The Brothers of Italy, which holds Eurosceptic and anti-immigration views, won 26 per cent of the vote in the September polls, compared with 8 and 9 per cent, respectively, for allies Forza Italia and the far-right League.
Ms Meloni's appointment is a change for the eurozone's third-largest economy and for the party, which has never been in government.
The consultations to cobble together a government have been overshadowed by disagreements over Ms Meloni's support for Ukraine since the Russian invasion, with her two would-be coalition partners both considered to be close to Moscow.
Ms Meloni has been firm about her support for Ukraine, in line with the rest of the EU and the US.
“I intend to lead a government with a clear and unequivocal foreign policy line,” she has said. “Italy is fully, and with its head held high, part of Europe and the Atlantic alliance.
“Anyone who does not agree with this cornerstone will not be able to be part of the government, even at the cost of not forming a government.”