Just forty-eight hours ago Italy had looked to be on course for snap elections after coalition talks between the anti-establishment Five Star Movement and the far-right League collapsed over the weekend.
The new government must now win confidence votes in parliament, expected to happen next week, Ansa news agency reported.
The coalition deal turns the page on months of political turmoil following an inconclusive election in March which had raised jitters among Italy's European partners.
But on Wednesday, Five Star leader Luigi Di Maio, who had called for Mr Mattarella's impeachment following his rejection of Mr Savona, offered an olive branch by proposing the controversial 81-year-old financier for another government post.
Italy has now been without a government since March, when its elections failed to produce a party capable of forming government on its own.
Finally, they agreed on Giuseppe Conte, a law professor, as the recommendation to President Sergio Mattarella to lead the Council of Ministers, after both parties held internal polls to vindicate support for their program.
Premier Giuseppe Conte and his newly sworn-in Cabinet had places of honor to view the pomp-filled military parade and Italy's aeronautic acrobatic squad.
The country's new populist, euroskeptic government is likely to be met with alarm by other European leaders, including French President Emmanuel Macron and German Chancellor Angela Merkel, who are both eager to push for further EU political and economic integration.
According to NPR's Jim Zarroli, "Although the two parties say they are not considering a departure from the eurozone, the mere suggestion of such a move has [also] scared investors".
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The Times-Picayune reports that Duplantis made the pitch to his followers in the May 21 edition of his weekly video address. He can fly around the world on his current jet, but he can't do it without stopping to refuel.
The parties have vowed to use their parliamentary majority to sabotage any government with Cottarelli at the helm, raising the specter of another national vote as early as July.
Financial markets bounced back on Friday after a rollercoaster ride this week. He said Italians needed to work harder, be less corrupt and stop looking to the European Union to rescue the country's poor regions."Italians have to take care of the poor regions of Italy.
But I no longer accept that everything which is going wrong in South of Italy, in Mezzogiorno, is explained by the fact that the EU or the European Commission would not do enough", he said after leaving a meeting in Brussels.
'The new government will make sure that the rights and the dignity of 60 million Italians will be respected, ' Salvini said in a statement, adding that 'Italians expect from Europe cooperation and not insults'.
28 May: In a day of rapidly moving events, Mr Conte takes his cabinet choices to Mr Mattarella but the president vetoes the choice of Paolo Savona as finance minister.
Luigi Di Maio, the leader of M5S, will head the super-ministry of Economic Development and Labor.
The appointment also riled populists whose attempts to form a government were quashed by Mattarella over their designation of a euroskeptic economy minister.
The Milan stock exchange jumped almost 2.5 per cent as banks hit hard by the turmoil showed signs of recovery.
"We'll get to work to create work, for those who don't have it, for those that do but without dignity", Di Maio said.