E! News said Friday the couple named their newborn Gio Grace Levine.
No other details, including the date or location of the baby's birth, are available at this time, reported People magazine, which also confirmed the child's arrival and name.
Gio Grace has a 16-month-old sister named Dusty Rose.
"Adam and Behati cannot wait for their second child," a source told Us Weekly when Levine and Prinsloo announced the pregnancy in the fall. "Adam is literally the happiest ever."