The mummy blogger welcomed her baby boy, the first with husband Denim Cooke, via c-section on Monday June 28.
"Raja. Born at 2.46pm 38 weeks 4.2kgs. We couldn’t have dreamt a more perfect baby,"she captioned the first photo of her baby breastfeeding.
"Love you so much Denzy The Cooke Trinity 💗💗💗💗 we are blown away with support from you all 💗".
Just one day before giving birth the author shared an emotional letter to her unborn baby.
"The minute your dad and I got together we knew you were coming," she started.
"We talked about you, joked about you and even picked out some names. Your dad told me he’d had a sign from the gods... I smiled, took another sip from my wine and proceeded to comb out his dreadlocks."
She continued, "This huge chaotic family of soon 7 kids, 2 dog and 2 madly in love parents has a place for everyone. Your place for the time being is in my arms. And I simply cannot wait to sniff you tomorrow."
Constance has four kids from a previous relationship and Cooke has two.