"I'm so excited for them both," she said, smiling broadly. "It's a wonderful event. Everybody's absolutely thrilled as you can imagine.
"I never expected to feel quite this happy but I've had a big smile on my face ever since the news broke."
When asked by reporters if she had spoken to the new parents she said "Not yet, i've sent messages but i'm hoping in the next couple of days to catch up with them.
As the mother of two children herself, Prince Edward's wife was very understanding of the situation of new parents.
"I think they'll probably just want to be together at the moment," the 48-year-old told members of the press.
"Having had babies myself I know that you really want to close down the hatches and just be together with your immediate family in the first few days and weeks.
"I hope to be able to see the baby some time soon but not just yet."
Sophie, dressed for the warm weather in a white dress, was at an event for the British Wheelchair Basketball at Swiss Cottage Sports Centre. She is a Royal Patron of the charity.
The Duke and Duchess of Cambridge's royal baby was delivered by the same doctor that cared for Sophie during the birth of her daughter Lady Louise Windsor and son James, Viscount Severn.
Sophie Wessex and Dr Marcus Setchell
Mr Setchell, who described future King as a "wonderful baby, beautiful baby," also cared for Sophie following her ectopic pregnancy in 2001.
As the rest of the royal family go about their daily lives, William, Kate and the infant son remain in the Lindo Wing at St Mary's Hospital, Paddington.
A Kensington Palace spokesperson said they were "all doing well" on Tuesday morning. The new family are expected to remain at the hospital until after 6pm on Tuesday night or Wednesday morning.