Sophie and Jamie became parents to a baby girl called Lyra on 2 March.
In a brief statement, they said:
"Musician Jamie Cullum and his wife, the author and presenter Sophie Dahl, have become parents.
"Their daughter Lyra was born on March the second. They are over the moon."
The famously private couple will not be releasing any further details about their daughter, including her weight or where she was born, according to their spokesman.
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