He went on to tell fans, "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, and Caspar, 29, were wed in August 2019, one year after becoming engaged.
They confirmed they were expecting in a Vogue interview in February of this year, with Ellie telling the magazine, "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."
At the time, she said she was 30 weeks along, and shared lovely pregnancy photos of herself in a long, white dress.
On April 1, Goulding shared two photos to Instagram, one a glamorous pose and one a more candid snap, captioning them, "Instagram vs. reality."