Pessina Costruzioni will build the first three 1,000-bed hospitals in Tehran.
Two other 500-bed facilities will be provided in Rasht and Nishapur.
Italian industries have high hopes following the lifting of sanctions against Iran on Saturday after the nuclear deal took effect.
In November, deputy economic development minister Carlo Calenda led a large business delegation to Tehran representing 178 companies, 20 business associations and 12 banking groups.
"Italy was Iran's leading economic and trade partner before the sanctions," Italian economic development minister Federica Guidi stressed a few months ago, seeking to ensure her country regains that position.
Before the sanctions took effect, trade between the two countries amounted to €7.0 billion ($7.7 billion), compared with about €1.6 billion at present, including €1.2 billion in Italian exports.
Iranian President Hassan Rouhani is expected to visit Italy and France from January 25th to 27th.
His visit was originally scheduled for mid-November but was postponed because of the attacks in Paris.