Little Pearl weighed a healthy 8 pounds, 6 ounces at birth.
The entire Osbourne family, including Jack's mom, Sharon, and sister, Kelly, have been anxiously awaiting Pearl's arrival, and tell Us Jack will be a terrific father.
"He's very nervous, but nervous-excited," Sharon, 59, told Us on Thursday. "He'll be a very good dad. I think he'll be very strict, but he'll be a very good dad."
Auntie Kelly can't wait to spoil her niece with the most comprehensive baby wardrobe in town!
"I already told him that this baby … is going to be the best-dressed baby there is," Kelly 26, has said. "'You're not buying the clothes -- I am!'"
The youngest child of Sharon and Ozzy Osbourne, Jack, 25, announced his engagement to aspiring actress Stelly in September and confirmed her pregnancy two weeks later.
Us Weekly --