The new parents have named their daughter Pearl.
The news was exclusively revealed by HELLO! magazine's editor Rosie Nixon on Tuesday night via her Twitter page.
"Big congrats @MrJackO & @lisamarstelly who today welcomed baby Pearl into the world. She weighs 8lb6oz & all are doing well!" wrote Rosie.
Kelly Osbourne, Jack's sister, retweeted the news, calling herself "one proud auntie".
She added: "Today has been one of the most amazing days of my life!"
Jack's mum Sharon said she felt overwhelmed at becoming a grandmother. "Today I witnessed my first grandchild being born, life changing experience. She is an angel."
Jack, 26, asked aspiring model and actress Lisa to marry him after a whirlwind four-month courtship.
"The most amazing man I've ever met asked me to marry him... and he wasn't joking! Crazy, right," said Lisa, also 26, announcing the engagement on Twitter.
Two weeks later the couple announced their baby news.