Little Pearl weighed a healthy 8 lbs., 6 oz. 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 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 their pregnancy two weeks later.
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