The socialite, who is the daughter of Bob Geldof, one of the founders of Band Aid, and her husband welcomed their second child on the same day as her late mother Paula Yates' birthday, reported Sun online.
"They are absolutely over the moon about their new arrival. It all went smoothly and Peaches will be in hospital for a while to recuperate. Bob is absolutely over the moon -- the whole family are," a source said.
"They are particularly pleased about the significance of the date as it makes Peaches feel she is keeping her mum's memory alive," it added.
Little Phaedra's date of birth marks what would have been Paula's 54th birthday. The former 'Big Breakfast' host died from a drug overdose aged 41 in 2000.
The 24-year-old star's siblings, Fifi, 30, Pixie, 22, and half sister Tiger Lily, 16, have reportedly been close by at her hospital bedside since giving birth.
Peaches, who married SCUM rocker Tom last year, is thought to have named her new bundle of joy after her favourite band Tangerine Dream's 1974 album, 'Phaedra'.
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