"Very happy morning all," wrote Kate on Twitter. "A little bit of 'news' - Mike & I very happy to share that Clemency is set to become a big sister this summer."
"Mike and I beyond thrilled - and once again totally surprised and blessed by Mother Nature."
"Having trouble keeping up with your lovely tweets," added Kate, as she was deluged with messages of congratulations. "Thank you all so much we are indeed absolutely thrilled and feeling very very blessed."
Kate also shared a photo of her baby's scan, which showed the expected arrival giving a thumbs-up.
"Wouldn't usually tweet a scan photo," wrote Kate. "But this was too sweet - baby gave us the 'ok' him/herself."
Kate's famous friends were quick to send her their best wishes.
"@katesilverton1 gorgeous photo. Great news. X," tweeted presenter Gabby Logan. "Really thrilled for you. Funny I said to Kenny the other night you looked amazing on the news. #blooming."
Katy Hill also expressed her excitement for the expectant mum.
"@KateSilverton1 ooh - I hear you have amazing news!" She wrote. "HOW EXCITING! Hugs to you sweet lady x."