Italy's political instability over the last few months has put other EU members on edge, concerned that this new government may leave the union and the Euro, which could precipitate the collapse of the EU.
Italy has avoided a damaging second national election after Giuseppe Conte was named prime minster of a coalition of the country's two anti-establishment parties.
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.
Italy's populist parties finally reached a deal to form a coalition government on Thursday evening after almost three months of political deadlock - a prospect likely to chill the European Union and shake financial markets.
Days after taking workplace, the 2 pillars of Italy's first populist authorities are already campaigning.
The dispute focused attention on the pro-Russia agenda of the euroskeptic League and 5-Star Movement government, which was sworn in last week and faces confidence votes in Parliament on Tuesday where its Russian Federation policy may come up.
"Look at this spectacle!" marveled 5-Star leader Luigi Di Maio moments before the swearing-in ceremony.
The foreign minister will be pro-European Enzo Moavero Milanesi, a former minister for European affairs.
31 May: Five Star and the League say they have agreed to restart coalition negotiations.
On Friday, a beaming Di Maio stood before Mattarella and recited the loyalty oath - he'll serve as minister of labour and economic development.
After the swearing-in, Salvini told reporters his first order of business would be to "reduce the arrivals and increase the expulsions" of migrants, as well as the costs associated with their care.
At 13 500 so far this year, refugee arrivals in Italy are down.
The new minister for public administration is defence attorney Giulia Bongiorno, a centre-right lawmaker legendary for defending ex-Premier Giulio Andreotti against mafia collusion charges and more recently, defending the ex-boyfriend of American student Amanda Knox against murder charges.
The changing of the guard sets the stage for obligatory confidence votes in Parliament next week.
Italian media reported that the lineup will face a vote of confidence on Monday or Tuesday in both houses of parliament, which it is nearly certain to win thanks to Five Star and the League's combined majority in parliament. In Italy, opposition politicians see the new government contract as "dangerous" and "illusionist".
The new government delighted leaders of an increasingly bolder far-right in European politics.
A crowd of enthusiastic supporters and a smaller group of protesters had earlier gathered in front of the gates of the town's migrant centre, where Salvini would give his speech, trading insults and almost coming to blows.