Mr Gentiloni, 62, succeeds Matteo Renzi, who resigned after losing a referendum eight days ago.
Pier Carlo Padoan remains economy minister and Angelino Alfano becomes foreign minister.
Mr Gentiloni is a loyalist from Mr Renzi's Democratic Party (PD), and he is expected to largely follow the former administration's programme.
The new government was sworn in by President Sergio Mattarella on Monday evening.
Mr Gentiloni faces a banking crisis and a rise in popular support for anti-establishment and eurosceptic parties.
Mr Renzi stepped down after Italians voted against his proposed constitutional reforms.
Opposition parties have ruled out joining a national unity government. The populist Five Star Movement says it will boycott a parliamentary approval vote, expected to take place this week, saying it would have no legitimacy.
Italy's new Prime Minister Paolo Gentiloni has taken office and announced his new cabinet.