The move, which will also apply to countries in the Schengen Area, came as the Italian government announced plans to ease travel restrictions to allow people to move freely inside the country from the same day.
In a bid to slow its epidemic, Italy was the first European country to impose strict nationwide restrictions in March and only allowed a slight relaxation of the rules on 4 May, when it allowed factories and parks to reopen.
Some regions had called for a swifter rollback of restrictions but Giuseppe Conte, Italy’s prime minister, has insisted on a gradual return to normal due to fears of a second wave of infections.
However, on Saturday he outlined a further loosening of restrictions including a plan to open borders to travellers from Europe next month.
With shops as well as bars and restaurants due to reopen from Monday, the government also announced that people will no longer have to justify travel within their own region and will be able to meet friends as well as family.
"People will be able to go wherever they want - to a shop, to the mountains, to a lake or the seaside," Mr Conte said.
The announcements came as daily coronavirus deaths in Italy, which has the third-highest number of fatalities in the world, fell to 153 on Saturday, the lowest since 9 March.
More than 31,600 Italians have died from Covid-19 since February, putting Italy's death toll behind only the US and the UK.
Shops are due to reopen and movement within individual regions will be allowed from 18 May, meaning people will be able to visit their friends.
While large public gatherings will still be banned, church and other religious services can resume and museums and galleries will also be able to open.
Gyms, swimming pools and sports centres will reopen on 25 May, while theatres and cinemas can reopen from 15 June.
The further lifting of travel restrictions will not come into effect until after Italy’s 2 June Republic Day to prevent any mass travel over the long holiday weekend.
From 3 June, travel will only be restricted if an area is considered to be at high risk for coronavirus infections, a move which offers some hope ahead to the country's vital tourism sector ahead of summer.
Regions will also be allowed to reactivate all sectors of the economy, so long as strict safety protocols and social distancing measures are followed.
Restaurants will be able to reopen so long as customers are kept at a distance of one metre from each other, with mandatory face masks for both staff and customers when they are not sitting at tables.
Mr Conte said the decision to lift curbs was a "calculated risk", but added: "We're facing this risk and we have to accept it because otherwise we will never get started again."