"It's of Etruscan origin," Berti, who also is Bocelli's manager, told the magazine about their newborn's name, Virginia. "The thing I like about this name is that none of my friends has it."
Bocelli, 53, has two sons -- Amos, 17, and Matteo, 14 -- from a previous marriage.
"With a dad and two older brothers she will have very attentive bodyguards," Berti said of little Virginia.
Exactly when and where the baby was born were not reported.