Travel for any reason, including tourism, to and from the following states is freely permitted:
Member States of the European Union: Austria, Belgium, Bulgaria, Cyprus, Denmark, Estonia, Finland, France, Germany, Ireland, Latvia, Lithuania, Luxembourg, Netherlands, Poland, Portugal, Czech Republic, Romania, Slovakia, Slovenia, Sweden and Hungary;
Non-EU States party to the Schengen Agreement: Iceland, Liechtenstein, Norway, Switzerland.
Other States included in the free circulation: United Kingdom of Great Britain and Northern Ireland, Andorra, Monaco Republic of San Marino and Vatican City State.
If you have been in any other State in the previous 14 days, you have to quarantine.
France, Croatia, Greece, Malta, Spain: the Minister of Health, with an Ordinance of 12 August 2020, in addition to what is already provided for EU countries, has established that those who enter/return to Italy from these countries (after a stay or even only transit) from 13 August and until further notice, must also:
a) present a statement that they have undergone a molecular or antigenic test carried out by means of a swab and a negative result within 72 hours before entering the national territory;
b) undergo a molecular or antigenic test; to be swabbed upon arrival at the airport, port, or border location (where possible) or within 48 hours of entering the national territory at the reference local health unit.
Persons who have stayed or transited in these four countries shall also communicate their entry into the Italian territory to the Prevention Department of the competent Health Authority.
See below more about the registration and swab.
Notice: On July 24, the Minister of Health signed an ordinance that requires to undergo the quarantine period for citizens who come from/have stayed in Romania and Bulgaria for the past 14 days.