Video clips show a close-up of the adorable newborn’s face as he sleeps soundly though his first hours on earth.
Denim took to his own Facebook page – The Cooke Trinity – on Monday to share a snap of his newborn son, alongside a poignant message.
‘Raja Wolf Cooke-Hall was born today at 2.46pm. At 9lb 5oz and 56cm tall he is perfect in every way,’ the proud dad wrote.
‘Con is sitting up in bed breastfeeding him at the moment and I couldn’t be prouder of her strength and bravery today and throughout this entire pregnancy.
‘Raja is absolutely adorable and feeding already and about to nap. He has barely cried and seems really content. Fingers crossed he remains chill.
‘Thank you for all the well wishes and thank you to my beautiful wife for this amazing gift ... you are a warrior woman and this child unites our crazy clan. I feel so lucky I could jump over the moon.
‘Oceanz of love to you all and stay tuned for some better pics later. Denim x.’
Earlier, Constance had shared some more candid snaps from hospital as she prepared to welcome her fifth child.
One clip on Instagram Storeis – which had the words ‘Baby Time’ written over the top in blue lettering – appeared to show Constance being prepped for surgery on Monday afternoon.
Constance also took to Instagram the day before her scheduled caesarean to welcome her unborn baby to the world.
'We don’t know anything about you, you might be wild and challenging of everything society throws at you like us or you might wear a suit, brush your hair and get 4 degrees,' she shared.
'You might be a tough and tumble sporty boy like your dad or an emotional artsy person like your mum. Or you could always be both.. You might even decide you don’t want to be a boy. We don’t care. We just want you.
'But what I do know is that last night your dad told me that the hardest park of this extremely painful pregnancy for him has been watching me in pain and not be able to take that pain away from me and swap it for himself.
'And that’s what I want for you, deep meaningful connections with your friends, your siblings, us, your dog, a lover.. don’t settle until you find someone who’s hurt hurts you and who’s smile makes you laugh.
'We don’t own our kids, you’ve just entrusted us to guide and protect you for a while. And we will do that. This huge chaotic family of soon 7 kids, 2 dog and 2 madly in love parents has a place for everyone.'