He wrote: “Not the 24hrs I had imagined. But ya never know what life has in store. This little guy is an absolute Trooper.
“I’m blown away with his strength and charm. Mum & Dad are a mess worried sick and he takes it in his stride.
“I am so incredibly grateful to the staff @chelwestft you guys rock.”
His wife has yet to break her silence on the trip to the London hospital.
From the hospital bed, the little boy could be seen passing the time watching Spiderman on his laptop and playing Minecraft in the two photographs shared on Instagram.
Mr Keating tied the knot with his second wife in 2015 and the couple have been living their happy ever after; they have two children together, Cooper and Coco.
The singer has three children - Jack, Marie and Ali - with his first wife Yvonne Connolly from their time together; the exes finalised their divorce in 2015.
Last year, Mr Keating described himself as a “hands-on” dad as he took extended parental leave after his youngest Coco was born.
He told The Sun at the time: “The plan was to take a three-week holiday, but it has turned into four months.
“It’s been amazing to be there for every single moment, from waking up in the morning, looking at her, to every bath and bedtime.
“It’s been a very special experience to witness her progress every single day.”