This document by Italy's Ministry of Health states that
Movements to/from EU countries (except for Romania and Bulgaria) are allowed without the need of justification, therefore also for tourism, and without the obligation of isolation on return provided that you have not transited or stayed in the territories belonging to lists C, D, E, or F in the 14 days prior to entering Italy. The requirement to fill in a self-declaration remain.(Except for the Republic of San Marino and the Vatican City State)
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:
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.
So my understanding is that I'll need to take a test in the airport, but I don't know if I have to wait for the test results in my hotel or I can move freely unless they call me telling me that I tested positive.