Matteo Renzi resigned after losing a referendum on constitutional reform last week.
The 62-year-old former foreign minister is a loyalist from Matteo Renzi’s Democratic Party.
Correspondents say that if Gentiloni is successful in rallying support a government could be formed in days.
In a brief acceptance speech, Paolo Gentiloni said he realized the urgency of forming the government to reassure the country.
The new prime minister said he would work within the framework of the previous administration, making it likely that he will reappoint several ministers.
Paolo Gentiloni faces a banking crisis and a rise in popular support for anti-establishment and eurosceptic parties.
Opposition parties have ruled out joining a national unity government, with the populist Five Star Movement saying it will boycott a parliamentary approval vote, due to take place on December 14, because it would have not legitimacy.
The party has called for immediate elections, currently due to be held in May 2018.
However, President Sergio Mattarella has said the current electoral rules must be revised so both houses of parliament are synchronized.
The law was changed to the so-called “Italicum” system last year to give the leading party a parliamentary majority through bonus seats in the lower Chamber of Deputies. But there has been no such change in the Senate, which is elected by proportional representation.
Senate reforms formed part of the package of reforms put to Italian voters on December 4, while the legitimacy of the system for the Chamber of Deputies is to be ruled on in January.
Matteo Renzi’s plans for constitutional reform were rejected by a margin of 59% to 41%, prompting his decision to stand down.
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