The baby boy is Ozzy and Sharon Osbourne's fifth grandchild.
Sharon spilled the beans during an appearance on the British chat show, The Talk, on Tuesday, revealing the little boy's name is Sidney, seemingly named after his father.
"So great, so great. She won't let a picture go out of him, and I'm so proud of her," Sharon shared of Kelly's experience as a new mom.
Sharon did not reveal exactly when Kelly gave birth, but in November Kelly sparked speculation she'd gone into labor by posting a cryptic message to her Instagram Stories.
At the time she simply wrote, "OK, here we go," on a black backdrop. She has been silent on social media ever since.
Kelly, 38, announced she was pregnant in May when she took to Instagram and posted photos of herself holding a sonogram.
"I know that I have been very quiet these past few months so I thought I would share with you all as to why," she wrote. "I am over the moon to announce that I am going to be a Mumma. To say that I am happy does not quite cut it. I am ecstatic! 🤰💜."
Shortly after Kelly's post, Wilson followed suit with a photo of the ultrasound machine. The 45-year-old Slipknot DJ captioned the post with only a series of emojis, "💕❤️👨👩👦❤️💕."
Osbourne and Wilson are longtime friends who have been dating for some time now. On Valentine's Day, she professed her love to the musician on Instagram, writing, "After 23 years of friendship I can’t believe where we have ended up! You are my best friend, my soulmate and I am so deeply in love with you Sidney George Wilson. 💜."