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The art dealer announced the good news on his Instagram Stories, first by posting a screenshot of the world's population in 2021 with the last digit changed from 5 to 6 to symbolise the new addition to their family.
He then posted a short statement confirming that mother and baby are "both healthy and happy" and requested privacy. He did not reveal the baby's gender.
He said: "I don't ever address the public attention that comes with Ellie's job. But during this magical and personal moment we would really appreciate being able to enjoy our privacy.. thank you x".
Ellie, 34, announced her pregnancy in February after discovering she was expecting on their first wedding anniversary in August in the month after she released her fourth album Brightest Blue. In an interview with Vogue, when she was 30 weeks pregnant, she said the news had been a surprise.
"It was crazy because it was our one-year anniversary. That was not the plan. The thought of getting pregnant didn't seem like it could be a reality. Becoming pregnant kind of made me feel human. I want a better word than womanly, [but] - I have curves I've never had before. I'm enjoying it. My husband's enjoying it," she said.
Ellie also discussed the sickness she experienced during her pregnancy, adding that it was like "nothing she has experienced before."
"The sickness and tiredness was nothing I'd ever experienced before. I feel like it's a taboo to talk about pregnancy as being challenging. It's not always serene and like you're not always glowing. I'm not saying that every second of this pregnancy has been miserable. It's not always going to be easy. [But,] I have a newfound respect for any woman who has children," she added.
Ellie and Caspar married in August 2019 at York Minster, with a host of high profile guests including Katy Perry and Orlando Bloom, Princess Eugenie, Princess Beatrice and Joe Wicks.
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