The unprecedented measures covering the entire Mediterranean nation of more than 60 million people came into force after Italy reported 97 more deaths that took its toll to 463.
An AFP count showed Italy with more than half of the 862 deaths reported outside China as of Monday night.
"I am going to sign a decree that can be summarised as follows: I stay at home," Conte announced in a dramatic evening television address.
"The whole of Italy will become a protected zone," he said.
The measures extend a quarantine zone that Italy had imposed for its industrial northern heartland around the cities of Milan and Venice on Sunday.
The national restriction will run until April 3 and mean that schools and universities will all immediately close.
Travel in and out of the country as well as movement between cities will be restricted.
But it was not immediately clear how all these measures will be imposed.
Trains and numerous flights continued to operate into and out of Milan on Monday despite the earlier set of restrictions for its Lombardy region.