You will be contacted by the Italian authority through which you submitted your application for citizenship. Though this may vary from country to country, you will probably receive an email or a letter stating that you have been recognized an Italian citizen and what is the procedure in order to receive an Italian passport. You will be registered in the Registry of Italians Resident Abroad (A.I.R.E.).
A.I.R.E. was established by Law no. 470/1988 and keeps track of the changes in citizenship status, address, marriage, birth and death of Italian citizens. A.I.R.E. enrolment is obligatory for Italian citizens living abroad for more than 12 months and for Italian citizens residing abroad either as a result of being born there or having obtained Italian citizenship through Ancestry (jure sanguinis), marriage or other.