The 50-year-old announced the news on Instagram as she shared a picture of her hand holding the baby’s feet.
“A beautiful little blessing has chosen me to be her mother, so honoured to have this gentle soul in my life,” she posted on the social media website.
Designer Marc Jacobs was among those to congratulate the London-born model, who had not previously revealed that she was to become a mother.
British Vogue editor Edward Enninful also offered his congratulations, writing: “Seeing the two of you together made my year. You will bring each other so much joy.”