The health certificate proves bearers have either been vaccinated with at least one dose, have recovered from Covid-19 within the past six months, or have tested negative in the previous 48 hours.
Under the new decree law, school and university staff will need the pass, as will university students.
Staff without passes for five days straight will be suspended and have their pay frozen, Italian media said.
Education minister Patrizio Bianchi told a press conference that over 86 percent of school personnel had been vaccinated, and that the number may be closer to 90 percent.
Health minister Roberto Speranza called on families to give the jab to children over 12 years old, and said teenagers would be eligible for cut-price rapid covid detection tests.
The green pass will be obligatory on domestic flights, trains and some ferry services from September 1.
Speranza said the pass — which has sparked protests in some quarters — was key to curbing rising Covid-19 cases, and he urged Italians to carry on getting vaccinated.
“The numbers are encouraging, with 70 million (vaccine) doses administered,” Speranza said, adding that the use of the green pass would “avoid closures and protect freedom”.
The minimum quarantine period for people who test positive for the virus or have been in contact with a COVID-19 patient was reduced for those who have been vaccinated, from 10 to 7 days.
Italy was the first country in Europe to make it obligatory for doctors and health workers in the public and private sector to get vaccinated or face being banned from working directly with patients.
A group of 300 Italian health workers has gone to court to try to get the obligation overturned.
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