The little boy was pictured chuckling to himself, showing off a wide gummy smile and dimples.
Jamie wrote on Instagram: "Smile Haha River's First proper smile. Brilliant who knows what's going though his head but I like it. Big love guys have a good day I send you a smile with love jo xxx."
"Brilliant, who knows what's going though his head," wrote Jamie
Jamie's post comes after he spoke to Sarah Brett and Nihal Arthanayake on BBC Radio 5 live Afternoon Edition. The restaurateur revealed that after all the sleepless nights and his hectic filming schedule, he and his wife Jools had decided to hire a night nurse.
"Sleep deprivation makes the most wonderful people just, unreasonable," said Jamie. "It hit us hard this year, really hard, because you know we've got two teenagers and it's teenagers things, and you've got a six and a seven-year-old as well, and they're up as well."
He added: "I've got a night nurse. She started a week ago, so five weeks in, so you know, we got battered for five weeks, and I was trying to help out, and do the night feed, and then go and do 15 hours of filming at the end of Southend pier, and that was tough."
The TV chef revealed that he and Jools had hired a night nurse
The celebrity chef shared a beautiful family photo with Jools and their three youngest children. "It's probably polite to formally introduce the new boy to you, his name's River Rocket Oliver we think it suits him and he's a little gift and we are all very happy," wrote Jamie.
While the couple were hesitant to share River's name so early on, Jamie and Jools have been posting plenty of images on social media.
They announced his arrival just hours after Jools gave birth, with Jamie exclaiming: "And then this just happened guys !! IT'S A BABY BOY !! Everyone in the Oliver family is very surprised and beyond happy."