According to Italian media the populist line-up will face a vote of confidence in both houses of parliament on Monday or Tuesday.
Conte, a law professor plucked from relative obscurity to head an unlikely governing alliance of the anti-establishment 5-Star Movement and right-wing League party, said the celebrations Saturday transcended all the tensions of recent days.
M5S leader Luigi Di Maio and League leader Matteo Salvini will join the government as deputy prime ministers.
The old order in the euro area's third-biggest economy buckled at the March elections as the centre-left Democratic Party of ex-premier Matteo Renzi suffered its worst-ever result, and Silvio Berlusconi, 81, was eclipsed as leader of the centre-right by the more hard-line League.
Their pick for Prime Minister, Giuseppe Conte, abandoned his mandate to form a government on Sunday after Mattarella refused to allow Paolo Savona, an outspoken critic of the European Union, to take up the post of minister of economy.
The new, unorthodox government was sworn in Friday following months of political turmoil.
President Sergio Mattarella, who negotiated three months of political deadlock to finally find a workable government, presided over the ceremony in the opulent Quirinale Palace in Rome. In a Facebook post featuring a photo of the Five Star ministers, he said: "There are a lot of us, and we're ready to launch a government of change to improve the quality of life for all Italians".
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. The political stability relieved financial markets on Friday but Italy's European neighbors continued to express concerns about the euroskeptic bent and the heavy spending agenda of Italy's new government.More news: Jason Chaffetz: "I Think the Attorney General Should Step Down"
On Sunday, Mattarella rejected the appointment of Paolo Savona as finance minister.
Despite decrying Italy's long history of installing unelected technocrats, the parties suggested Conte as prime minister.
"We're ready to reconsider our position in the sense that if we made a mistake - something I doubt - we'll say so, but now we should respect the will of the people", news agency AP quoted him as saying.
Mr Tria has been critical of the EU's economic governance, but unlike Mr Savona he has not advocated a contingency plan for exiting the euro.
Mr Conte, whom the president had tapped as premier-designate before former International Monetary Fund official Carlo Cottarelli, relinquished his mandate. The sentiment regarding this decision, similarly to events regarding then-Prime Minister Mario Monti in 2011, is that it is an EU-engineered plot.
"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.
The Milan stock exchange jumped almost 2.5 per cent as banks hit hard by the turmoil showed signs of recovery.