The mother-of-four - who also has sons, Teddy, seven, and Charlton, five, with the pop star - captioned the Instagram post: "@robbiewilliams A Beau-tiful Moment #fatherandson #babybeau AWxx (sic)"
The couple announced the surprise arrival of Beau on the social media app on Valentine's Day.
Alongside a snap of the family's feet in a circle, Ayda wrote: "Spot the difference...'
"On this Valentine's Day, we would like to celebrate love in the most awesome way... Beau Benedict Enthoven Williams.
"As with Coco, he is biologically ours, but born via our same incredible surrogate.
"We are so blessed to have our healthy son safely in our arms and are officially complete as a family. #happyvalentinesday #surprise #familyof6 #whodathunkitinthe90s The Williams Family xx. (sic)"
Robbie, 46, previously spoke about fatherhood as he said the new job had changed him after a life of "strippers and cocaine".
He said: "Back in the 90s, it used to be strippers and cocaine and now it's hummus and celery and my life is much better for that.
"I used to live on rock star hours, which was go to bed at three or four o'clock in the morning, and wake up in the afternoon.
"You quickly realise when you have a child you are not an insomniac but a bit lazy and prone to exaggeration."
