The four bundles of joy – three girls and one boy – came into the world at 4:30 am.
They were born just 25 minutes apart, in the following order: Gina, Elena, Antonio and Elisabetta.
The babies were born around seven weeks premature and weighed between three pounds, three ounces and three pounds, 11 ounces each.
They will spend at least two weeks in the neonatal intensive care unit.
A group of 10 obstetricians attended to the birth of the quadruplets and will now ensure they receive the adequate care and nutrition.
Mrs Faella and her babies are all in good health, according to a spokesperson for the hospital.
She and her husband Michele, 39, migrated to Australia from Benevento, in the southern Italian region of Campania.
They have one other child: seven-year-old Aldo.
The couple have received many congratulatory messages, including one from Victorian Premier Henry Bolte and another from Immigration Minister Alick Downer.
Mrs Faella has also received many flowers and gifts from members of the Italian community.
The couple will now need to find a bigger home to accommodate their growing family.
Mrs Faella will receive a maternity allowance of £31, as well as £2 a week of family benefits.
Three other sets of quadruplets have been registered in Victoria – in 1917, 1949 and 1950.
In the first two cases, all four of the quadruplets died; in the third case, one of the babies didn’t survive.
