Dani, who was a finalist on the show's 17th series, which aired earlier this year, and her partner Rocky Oliver made the announcement on Instagram.
"Binky Bloom Oliver. 22.09.23. Our hearts are so full," reads the caption, alongside a photo of both parents on the sofa cradling their newborn.
"Aww Dani! I'm so happy for you and your new little family, going to be the best mum ever!," wrote Apprentice series 17 winner Marnie Swindells, while Reece Donnelly from the same series and Kathryn Burn from series 16 commented with their congratulations.
On her Instagram Stories, Dani shared a picture of Rocky outside the hospital with Binky in a baby carrier, and other photos and videos of the couple's loved ones cuddling the baby.
Dani isn't the only reality TV celebrity who gave birth over the last couple of days, as The Traitors and Hollyoaks star Maddy Smedley also became a mother.
She announced the news on her own Instagram page, sharing a photo of herself holding her baby in the hospital bed. "Welcome to the world Shelby Rae, love you so much already," she wrote.
The Apprentice is due to return next year, but there will be some changes, specifically the interviews round, which was seen as being too harsh.
"I think we need to tone that down a bit. I found it hard to watch," Lord Sugar said.
"Unfortunately when that was recorded, I wasn’t there. Anyway, I’m not making any excuses. When I saw it in the end, I thought, 'This is too harsh', and we’re going to tone it down now.
"I don’t think it’s entertaining. It used to be entertaining. All the previous boardroom [episode] 11s were entertaining. This one was very harsh."
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