The rules on travel have changed a few times, so it’s probably easier you check the current rules yourself.
You will need to fill in the European Passenger Locator form whatever country you travel from, but the rules do change depending on what else you need to do.
The Italian government has a really simple to use site that shows you what you need to do
COVID-19 SURVEY (viaggiaresicuri.it)
The actual legal decree currently in force as of 24th September 2021 is
English (UK) 
Italiano