Jess wrote back: 'The baby is amazing. Will post soooooon ish.'
'I’m very happy for you,' the fan responded. I was thinking it’s gotta be out by now. Enjoy the newborn bubble and congratulations on becoming a mum.'
Baby joy: On Wednesday, the former Victoria's Secret model posted a photo of a plush swan which appeared to be a baby gift
'The baby is amazing!' Jess also confirmed the birth of her first child on Instagram
Jess responded: 'Thank you.'
Jess and James confirmed their engagement in October.
The NASCAR driver popped the question in front of the model's family and friends at their beachside baby shower in Malibu, California.