The party was predicted to have anywhere between 25 and 31 percent of the vote, followed by the centre-left Democratic party in second place, according to exit polls published by broadcasters RAI and Mediaset and the TV channels La7 and SkyTG24.
Meloni's victory had been widely trailed given her success in September 2022 national elections, when Brothers of Italy won 26 percent of the vote, and her continued popularity.
In European Parliament elections in 2019 in Italy, her post-fascist party had secured just six percent of the vote.
Elly Schlein's Democratic Party was on course for between 21 and 25.5 percent of the vote, the exit polls indicated, while the Five Star Movement of former premier Giuseppe Conte was predicted to have between 10 and 14 percent.
Meloni's coalition allies, Matteo Salvini's far-right League party and the right-wing Forza Italia of late ex-premier Silvio Berlusconi, were projected to have between seven and 12 percent.
Salvini had topped 2019 European elections with 34 percent of the vote.
Meloni had held up the European vote as a referendum on her personal leadership, asking voters to write simply "Giorgia" on their ballots.
She stood for election herself but will not take up her seat, as being an MEP is incompatible with national political office.
If the results are confirmed in the coming hours, all eyes will be on what Meloni will do with her increased influence in Brussels.
She has been courted both by Ursula von der Leyen of the centre-right EPP group -- who is vying for a second term leading the powerful European Commission -- and France's far-right Marine Le Pen.
Le Pen's National Rally was projected to win around 33 percent in the elections, trouncing French President Emmanuel Macron's centrist alliance and prompting him to call snap legislative elections.
Meloni's party is in one of two main far-right groups in the European Parliament, the European Conservatives and Reformists (ECR), alongside Spain's Vox.
Le Pen is in the Identity and Democracy group, which also includes Salvini's League.
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