The Smile singer, who adopted her husband Sam Cooper's surname and became Lily Rose Cooper, gave birth on Tuesday (08Jan13), according to The Sun.
A source tells the tabloid, "Marnie is a real cutie. Sam and Lily are ecstatic about adding another girl to the family."
The couple already has a 14-month-old daughter, called Ethel.
The birth comes after a week of tweets in which the singer told followers she was desperate to give birth - even trying hot, spicy food to lure her baby out.
In one post, she wrote, "3rd curry this week... cosywomb."
The hitmaker, who is the daughter of actor Keith Allen, and Sam Cooper wed in June, 2011.