In another photo posted a week ago, the family look happy as they enjoyed a stroll outside in the sunshine.
In the caption, the chef confirmed his son's name was River Rocket Oliver, adding that he thinks the name is a good match for the tot.
"It's probably polite to formally introduce the new boy to you, his names River Rocket Oliver we think it suits him and he's a little gift and we are all very happy.... Thanks for all your kind wishes big love jamie and gang," he wrote.
The hands-on dad has been busy juggling fatherhood and his work at his various restaurants, as well as the impending launch of his new cookbook, Super Food Family Classics.
Although Jamie's job means he's often away from home, Jools says youngest daughter Petal, 7, is her little helper with the baby.
She recently posted a heartwarming pic to her Instagram page, showing her "cutest little sidekick" Petal helping to give River a bath.
-nzherald.co.nz
