"The Italians have entrusted us with an important task. Now it is our job to not let them down and do our utmost to restore dignity and pride to the nation," she wrote on Twitter.
Meloni is set to lead a conservative coalition into power as her populist Brothers of Italy party took an estimated 26 per cent of the vote in Sunday's poll.
She would be the first female prime minister in Italian history if her party agrees on a governing coalition with their right-wing partners Lega (almost 9 per cent) and Forza Italia (8 per cent), both of which lost favour with voters.
"Today we made history," Meloni tweeted earlier.
The progressive bloc led by the Social Democrats, the Five Star Movement and The Alliance of the Centre were unable to stop their opponents, which went into Sunday's election with more momentum.
"Meloni takes Italy," read Monday's banner headline on the daily La Repubblica.
Meloni spoke of a "night of pride" and basked in congratulations from conservative colleagues across Europe including French nationalist Marine Le Pen, the leadership of Germany's anti-immigration AfD party and Polish Prime Minister Mateusz Morawiecki.
Meloni is expected to receive a mandate to govern from Italian President Sergio Mattarella in the next couple of weeks and will then assemble her cabinet.
Coalition negotiations can only begin once the new parliament has started work in mid-October.
A government with the 45-year-old at the helm is expected to take action against Mediterranean migrants as well as fight against and renegotiate the conditions of the COVID-19 reconstruction fund in Brussels.Â
On the campaign trail, Meloni also promised tax cuts.
The head of Italy's Social Democrats (PD), Enrico Letta, on Monday said he is resigning after his party's loss.
The former prime minister said that he would not stand as a candidate for the post of general secretary at the PD's next congress.
Letta spoke of "a sad day for Italy" and said it was now the task of a new generation to form a strong opposition.
