"Yes just to say our little boy was born in the early hours of Thursday weighing 8lbs 3oz - we are just home and all very well indeed!
"His name is Wilbur - after the man who first inspired my love of #africa and its wildlife."
Kate then shared the first photo of her new arrival with the message: "Gorgeous morning all - Introducing #Wilbur our little ray of sunshine x."
Wilbur is Kate and husband Mike Heron's second baby. They are already proud parents to daughter Clemency, two.
According to our baby name finder, Wilbur is of Anglo-Saxon origin meaning 'dearly loved stronghold.' It is also derived from an Old English nickname meaning 'wild boar'.
Kate has previously spoken about her struggle to conceive, and went through four failed rounds before falling pregnant naturally with Clemency.
Speaking in April, Kate said: "I fell pregnant with Clemency, and that was - as we say - a miracle.
"Then I was terribly broody after Clemency and I just said to Mike 'I would just love to go through that experience again'. I did fall pregnant very quickly - and again very naturally - and sadly miscarried quite early, six weeks.
"I just thought, OK that's just one of nature's things and then a few months later I fell pregnant again."
Kate then went on to add: "There was a little message I sent to the stars. If I could just breast feed one more time, if I can go through labour one more time.
"I just thought I'm going to be kind to myself with acupuncture, lots of massages – nothing too much – just having a really sort of sanguine approach to it."
And it worked!
Congratulations Kate, Mike and Clemency!