Addari was born in Genoni, Sardinia, Italy on 25 March 1912 to Pietro Addari and Marietta Piroddi. She had six siblings, two of whom lived over a century: Amerigo died aged 101, and Giovanna died at 110 years, 28 days, making the two sisters among the oldest sibling duos of all time. Her father worked as an elementary school teacher, and her mother was a housewife.

Addari never married and had no children, instead pursuing hobbies such as crocheting. She moved from Genoni to the nearby town of Nuragus, and later became the oldest person in Sardinia after the death of her sister on 22 July 2020. She is currently the fifth-oldest person and second-oldest woman ever in Sardinia.