The ministers feature a mix of 5-Star and League loyalists and a political neophyte in the form of Premier Giuseppe Conte, who was still teaching his law classes at the university in Florence up until Thursday. The President has also approved a list of cabinet ministers brought by Conte to the palace.
Salvini, who promised during the election campaign to expel half a million illegal immigrants from Italy, is Italy's new interior minister, while Five Star leader Luigi Di Maio will become labor and economic development minister, a key position to fulfill his campaign promise of a universal basic income.
New Prime Minister Giuseppe Conte, 53, was sworn in at the head of the first populist government in an European Union founding member that was forged by the Five Star Movement and the far-right League.
Conte - a little known lawyer and political novice - announced his picks for the country's future cabinet after meeting with Mattarella.
Italian Premier Giuseppe Conte is cheered by citizens on the occasion of the celebrations for Italy's Republic Day, in Rome Saturday, June 2, 2018.
The League and Five Star proposed a government led by Conte last week.
Italy's premier-designate has said "new possibilities" have emerged over the forming of a government based on the outcome of the March 4 election.
Earlier this week, Sergio Mattarella invited former economist Carlo Cottarelli to form a government.
Luigi Di Maio, leader of Italy's populist Five Star Movement (M5S), has called for supporters to gather in Rome today as his party has salvaged its efforts at making a coalition with the right-wing Northern League.
Their first try failed when Mattarella rejected their choice of economy minister as dangerously euroskeptic.
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Eighteen ministers - five of them women - took the oath of office, pledging to observe Italy's constitution and work exclusively in the interests of the nation.
Europe's populists and right-wingers cheered the news as a slap in the face to Brussels, with French far-right leader Marine Le Pen tweeting: "Bravo to the coalition".
Salvini wrote: "Maybe, finally, we are there".
Just the prospect of a political government calmed markets Thursday. That sparked a breakdown of the coalition's first attempt to form a government and a furious reaction from the coalition leaders.
"The earlier we vote the better because it's the best way to get out of this quagmire and confusion", Salvini told reporters.
Italy's populist leaders are getting a second shot at putting together a government.
PM-designate puts technocrat government formation on hold to allow for possible compromise by populist parties.
Mr Salvini said late on Wednesday that he is not closing the doors on any solution but also indicated some resistance to the change, saying "if someone in Berlin or Paris wakes up in a bad mood that doesn't mean that an Italian minister gets kicked out".
Mattarella had vetoed Savona, a former industry minister who has questioned whether Italy should keep the euro, leading to the collapse of the 5-Star-League bid.
Markets had been wrestling this week with the implications of an Italian governing crisis, which sent its government bonds spiraling down earlier this week and hit the euro and other risk assets.