The Smile hitmaker welcomed a second daughter, Marnie, with husband Sam Cooper, and the tot shares a birthday with music legends David Bowie and Elvis Presley.
The singer, who is now known as Lily Rose Cooper, is currently recovering from the birth, but took to Twitter on Thursday to thank followers for their kind messages.
She writes: "Quite overwhelmed by all the well-wishing going on. Thank you everybody."
Little Marnie joins her elder sister Ethel, who is 18 months old.