"We will immediately start working to address Italy's burning needs," Meloni wrote on Twitter after 225 senators voted for the government and 79 against.
Meloni and her post-fascist party Brothers of Italy won 26 percent of the vote in the election.
The government coalition now also includes Matteo Salvini's far-right Lega party and controversial ex-prime minister Silvio Berlusconi's Forza Italia.
During her election campaign, Giorgia Meloni advocated, among other things, "natural" nuclear families and a total stop to refugee boats from North Africa.
Now she has repeated that message.
She does not want to see boats with migrants even able to leave Libya - the country from which most of the boats come.
- The people smugglers should not be the ones who decide who gets to come here, she says.
A thousand migrants were rescued
The issue came to the fore during the night of Wednesday, when the Italian coast guard rescued more than 1,000 migrants from two boats in the Mediterranean.
The boats had sent out distress calls three and six miles southeast of Sicily, respectively, and the rescue work is described as "complicated".
At least two people are said to have been found dead.
At the same time, two other rescue ships from human rights organizations have since Tuesday more than 300 migrants on board and they are not allowed to dock in Italian ports.
- The ships do not act in line with European and Italian regulations on border controls, says Meloni's newly appointed interior minister Matteo Piantedosi and announced that he was considering banning the ships from entering Italian waters.
"They know what we do"
The organization SOS Medelhavet, whose Ocean Viking is one of the ships, denies that they are breaking regulations.
- It is not true, it is not true at all, says Italy manager Alessandro Porro to Radio24.
The authorities, especially those in Italy, know very well what we do, where we do it, and they are constantly informed about our actions.
Who is Italy's new leader? See in the clip below.
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In 2008, Giorgia Meloni became Italy's youngest minister ever, when she took a seat in Silvio Berlusconi's government.
Photo: FABIO FRUSTACI/EPA