Published Monday, 07 May 2012
Osbourne's fiancee Lisa Stelly gave birth to daughter Pearl on 24 April and the couple has unveiled the new arrival in the latest edition of Hello! magazine.
The reality TV star's mother Sharon cradles the baby as Jack and his partner stand either side of her in one shot, and Jack insists he has never felt happier.
He says: "People say when you have a kid it's like instant love, but unless you've experienced it, it's impossible to comprehend. The moment I saw her I felt more love than I'd ever felt for anything. It was the weirdest, most overwhelming thing."
Osbourne also reveals he had only been dating Stelly for three months when they discovered she was pregnant.
He adds: "I think I responded with 'That's interesting'. What do you say? If we'd been trying for two years, of course you'd be like 'Awesome'. But we met in May and found out in August.
"I told Lisa: 'You need to give me a week to really take this in'. I had that time to get my head around the whole situation."
Sharon adds: "It's incredible to see Jack holding his baby girl, walking around so confidently. He's very nurturing and he and Lisa are so good together."