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Kelly Osbourne Says Dad Ozzy 'Told Everybody' the Sex of Her Baby on the Way: 'He's So Excited'

Mum's the word for Kelly Osbourne — literally!

While the 37-year-old tried to keep the sex of her baby on the way a secret, her father, rock legend Ozzy Osbourne, is so elated to be a grandfather again that he's having trouble keeping it in.

"Well, look, all I will say is that my dad has f------ told everybody," the first-time mom tells PEOPLE exclusively while discussing her partnership for the first annual National No Sugar Day on Oct. 3. "Because he's so excited."

The U.K. native and her musician boyfriend, Slipknot's Sid Wilson, announced on Instagram in May that they were expecting their first baby together.

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Kelly Osbourne pregnant
Kelly Osbourne pregnant

Kelly Osbourne/Instagram

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"I know that I have been very quiet these past few months so I thought I would share with you all as to why… I am over the moon to announce that I am going to be a Mumma," Osbourne wrote at the time. "To say that I am happy does not quite cut it. I am ecstatic! 🤰💜."

The former Fashion Police host explains that her 73-year-old father has had so much trouble keeping his mouth closed that he accidentally planted it in the press.

"If you just look up one of his interviews, you'll find the answers," Osbourne says. "Even though I'm not saying anything! He did an interview today and I'm outside the door. I'm like, 'Dad, shut up!' He tells everyone because he's so excited."

Earlier this week, the singer revealed she is expecting a baby boy in an interview with Entertainment Tonight.

Despite her dad driving her crazy by spilling the beans, she's feeling great heading into the home stretch of her pregnancy.

Exclusive... Ozzy Osbourne And Kelly Osbourne Shopping In Beverly Hills
Exclusive... Ozzy Osbourne And Kelly Osbourne Shopping In Beverly Hills

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"I am feeling really good," Osbourne, who's keeping her due date to herself, tells PEOPLE. "I am very close to the end of my pregnancy. When you think about, 'Oh, I'm going to be pregnant for nine months,' you think that's the longest time ever. It goes by so quickly, it's unbelievable."

One of the reasons she credits feeling so good? Cutting out certain sugars and carbohydrates from her diet.

As PEOPLE exclusively learned, the former singer was diagnosed with gestational diabetes in the third trimester of her pregnancy. The news forced her to take a look at her diet and get involved with launching the first annual National No Sugar Day alongside the No Sugar Company and its CEO, Brad Woodgate.

"Basically, I thought it was something that I had done wrong," Osbourne shares of her diagnosis. "I wasn't eating right. I didn't realize that it was actually my placenta blocking my body from breaking down sugar properly because I've never had any problems with sugar or anything like that. But I will tell you that now that I have been through this experience and what I have learned, I'll never eat the same way again."