The parliamentary election was held in Italy on March 4 and resulted in M5S securing more than 32 percent of the vote.
Mattarella had objected to the coalition nominating anti-euro politician Paolo Savona as Minister of Economy and Finances and used his veto as President to block Conte from forming government. The ceremony took place in Rome.
Yet migrant arrivals to Italy actually plunged in the previous year under the center-left Democratic Party, which signed controversial deals with Libya to beef up coastal patrols and prevent migrants from setting out in smugglers' boats across the Mediterranean Sea.
Newly appointed Italian Prime Minister Giuseppe Conte rings the bell during his first cabinet meeting at Chigi palace in Rome, June 1, 2018.
The government will be formally handed over later on Friday and will face a confidence vote later this week, which given the makeup of Parliament is likely to pass.
Mr Mattarella said he could not appoint the eurosceptic to the post, citing concern from investors at home and overseas.
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.
Stop-gap PM designate Carlo Cottarelli has stepped back from forming a technocratic government, reports say.
Giuseppe Conte had been approved for Italy's top office by the country's President Sergio Mattarella on Thursday evening after the right-wing League and anti-establishment Five Star Movement reached a coalition agreement. He has already promised to reduce the number of arrivals and increase the number of expulsions.
The new government delighted leaders of an increasingly bolder far-right in European politics.
The League has also faced widespread criticism for xenophobic, anti-immigrant policies reminiscent of those forwarded by far-right parties across Europe, such as Germany's AfD and the National Front in France. The populist coalition has a programme that pledges a spending spree and tax cuts, a guaranteed "citizen's income" for the poor, scrapping a pension reform which raised the retirement age, and challenging European Union rules. Nigel Farage, a British force behind the successful Brexit movement, advised Italy's populists to "stay strong or the bully boys will be after you".
The two populist party leaders are both deputy prime ministers as well as key ministers in the new government.
She pointed out that European Commission chief Jean-Claude Juncker recently called for the EU to find avenues where it can work with Russian Federation, saying "this Russia-bashing has to be brought to an end". Di Maio is also the minister for labor, a combination he said made sense since the two ministries must work together.