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 - 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 has12-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'.
Log in with your social accounts:
Or, log in with your IrishCentral account:
Don't have an account yet? Register now !
Join IrishCentral with your social accounts:
Already have an account ? Log in
Or, sign up for an IrishCentral account below:
Make sure we gathered the correct information from you
You already have an account on IrishCentral! Please confirm you're the owner.
Our new policy requires our users to save a first and last name. Please update your account: