Conte's appointment could herald an end to more than two months of political uncertainty in the eurozone's third-biggest economy - but the coalition's eurosceptic and anti-immigrant stance has alarmed senior European officials.
President Sergio Mattarella on Wednesday approved Conte's nomination to be prime minister of a government formed by the anti-establishment Five Star Movement (M5S) and the far-right League.
M5S member Conte survived a battering in the press over claims he exaggerated his CV.
On Thursday he was locked in consultations with delegations from political parties in order to put together the country's new government.
He said he would present his cabinet line-up within "the next few days", after a nearly two-hour meeting with President Mattarella on Wednesday.
The list of ministerial candidates must be endorsed by Mattarella before it can seek parliamentary approval.
Italian media reported that League chief Matteo Salvini would become interior minister while M5S leader Luigi Di Maio would be in charge of the economic development ministry.
Conte, a 53-year-old lawyer, struck a conciliatory tone towards Europe when speaking to journalists at the presidential palace.
"I'm aware of the necessity to confirm Italy's place, both in Europe and internationally," the prime ministerial nominee said, casting himself as the "people's lawyer".
"My intent is to give life to a government of the people that looks after their interests. I'm ready to defend the interests of Italians in Europe and internationally, maintaining dialogue with European institutions and representatives of other countries."
EU Economic Affairs Commissioner Pierre Moscovici said Wednesday it was a "good sign" that Conte had called for dialogue.
Mattarella had reportedly been concerned about plans by the two coalition parties to name staunch eurosceptic Paolo Savona as economy minister.
A joint government program unveiled by the parties on Friday pledges anti-austerity measures such as drastic tax cuts, a monthly basic income and pension reform rollbacks.
Di Maio and Salvini claim the measures will boost growth.
But EU officials have voiced concern that Italy could trigger a new eurozone crisis by refusing to stick to public spending and debt targets set by Brussels.
Moscovici had said on Wednesday that Italy must deliver a "credible" response on how it will reduce its debt, the eurozone's second largest in proportion to GDP.
The government program also includes plans to speed up expulsions of illegal immigrants and crack down on trafficking.
Nearly 700,000 people have landed in Italy since the migrant crisis exploded in 2013.
Bullish League leader Salvini has responded forcefully to criticsm of the program.
On Thursday he appeared to take aim at Brussels.
"Finally, we're getting off the ground. I hope there are no more attempts, from Italy or abroad to stop the change: Work first, security first," he tweeted.
"#ITALIANSFIRST. We will never again be anyone's slaves."
At the March 4 election, the M5S became the country's largest single party in parliament with 33 per cent of the vote.
The nationalist League won 17 per cent within a right-wing coalition that topped the polls.
Unhappy with the Five-Star League program, the League's former allies - including Forza Italia (FI), the party of political heavyweight Silvio Berlusconi - have placed themselves in opposition to the nascent government.
The coalition has a 32-seat majority in the lower Chamber of Deputies, but just a razor-thin six-seat majority in the Senate.
That could be reduced even further if senators such as Salvini are given ministerial roles.
Forza Italia has denounced the government program as "worrying".
The centre-left Democratic party (PD) said on Wednesday that it marked "the birth of a far-right government, with a far-right program."
Centre-left former premier Matteo Renzi said his PD party would be the "civil opposition" to Conte.