The little girl was born on Tuesday – the same birth date as Lily's musical heroes Elvis Presley and 66-year-old David Bowie.
Lily, 27, whose full name is Lily Rose Beatrice, was said to be 'ecstatic'.
The normally prolific Tweeter hasn't officially broken the news to her 4 million followers, but this morning she thanked well-wishers, Tweeting: "Quite overwhelmed by all the well wishing going on. THANKYOU everybody x x x".
One friend told the Sun: "Marnie is a real cutie. Sam and Lily are ecstatic about adding another girl to the family.
"A little sister for Ethel is brilliant news to lift the January blues for the family."
Friends were speculating Marnie had been named after Hitchcock's 1964 thriller Marnie. Rose is also Lily's middle name.
The Brit award winner, who now goes by her married name, was pregnant with Ethel - now 14 months - when she and building firm boss Sam wed in Cranham, Gloucs, in June 2011.
The previous October, tragically, she lost a baby son with Sam when she was six months pregnant.
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