"Charlie Joseph Robertshaw. Prepare to be loved," she wrote on May 23.
The new dad also shared a snap of his son, calling him: "Charlie Joseph Robertshaw The First."
Marni, who married David last year, is also mum to four-year-old Archie - who she shares with Dan.
Marni confirmed they were becoming a family of four back in November.
She told New Idea, "We are incredibly fortunate to be adding to our family. I cut it really close with the dress fitting and definitely lost my yoga stomach for our honeymoon, but it is all worth it!"
"It is something that was in our mind, but we wanted to wait until our life and home were settled, especially for Archie."