Yes. The agreement between Switzerland and the EU concerning the free movement of persons effectively includes Switzerland in the free movement system of the EU and EEA. In particular, it provides for the use of a national ID card in place of a passport.
Note, however, that there are some differences. For example, you will need a work permit because your contract is longer than three months. Some PDF "factsheets" are available on the website of the State Secretariat for Migration, also in Italian.
For further confirmation, you'll want to check the website of the canton where you'll be working (the federal secretariat has a list). For example, Geneva's application form asks for une pièce d'identité rather than un passeport.
To be clear, if you're not using a passport, you must use a national ID card that states your nationality. Other forms of identification, such as driver's licenses, are not sufficient.