The socialite - whose father is Sir Bob Geldof, one of the founders of Band Aid - and her husband Tom Cohen welcomed their second child, Phaedra, on Wednesday (24.04.13) - the same day as her late mother Paula Yates` birthday.
A source told The Sun newspaper: "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.
"They are particularly pleased about the significance of the date as it makes Peaches feel she is keeping her mum`s memory alive."
Peaches - who also has 12-month-old son Astala with Tom - gave birth via caesarian section on April 24 and reportedly planned to honour her mum with the birth of her first child last year, but missed the date.
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 S.C.U.M. rocker Tom last year - is thought to have named her new bundle of joy after her favourite band Tangerine Dream`s 1974 album, `Phaedra`.