Andy Rose Osbourne was born last Saturday, June 13, reported Hello! magazine.
Jack, 29, and Lisa's first child, also a girl, is three-year-old Pearl.
The duo announced they were set to add to their brood by sharing a photo of Lisa's blossoming baby bump on Jack's Instagram profile in February.
Lisa, 28, also revealed the news on her blog, Raddest Mom, at the time, writing, "Pearl is very happy to become a big sister. She diligently reads her 'I'm a big sister' books every night & recites to me her plans of bathing, feeding, singing to, and holding the baby.