Photos accompanying the name news showed the couple holding August, who wore a blue hat and was swaddled in a matching blanket.
In her caption, Eugenie also revealed that August was delivered by a midwife, who took the pictures of the new family.
“Thank you to the wonderful essential workers including our midwife who came to discharge our boy,” Eugenie wrote.
Eugenie, who is tenth in line to the British throne behind older sister Beatrice, 32, married Brooksbank at Windsor Castle in 2018, the same year and the same location Prince Harry and Meghan Markle tied the knot. The couple reportedly moved out of the Sussexes’ Frogmore Cottage home in December.