After the announcement, other stars posted messages of congratulations on Twitter. Model Daisy Lowe wrote: "Congratulations!! Loads of love yummy mummy."
Peaches kept her pregnancy a secret until January when she announced she was expecting a son on April 24 - the date which would have been her late mother Paula Yates's 53rd birthday.
Peaches, who was 11 when Miss Yates, a writer and broadcaster, died of a heroin overdose in September 2000, said of the due date: "I feel like it's a little wink from my mum."
Peaches and Thomas, who had been friends for five years before they began dating in December 2010, are due to marry this year.
It will be the second wedding for the wild-child star, who wed rocker Max Drummey in Las Vegas in 2008.
The marriage lasted six months.
- DAILY MAIL