Peaches Geldof gave birth to her second baby this week on what would have been her mother's 54th birthday.
The ex-TV presenter, who has another son called Astala with husband Thomas Cohen, had the child on Wednesday.
The couple, who married last year, had already decided to call him Phaedra.
A spokesman for the couple said: "Peaches Geldof and Thomas Cohen are delighted to announce the birth of their son on 24 April 2013. Both mother and baby are very healthy and well."
Speaking last year, Peaches Geldof said the baby's name was a nod to one of their favourite songs, Some Velvet Morning by Lee Hazlewood and Nancy Sinatra.
It contains the line "Some velvet morning when I'm straight I'm gonna open up your gate and maybe tell you about Phaedra".
Peaches Geldof confirmed she was pregnant with her second child in November.
The 24-year-old is the daughter of poverty campaigner Bob Geldof and the late Paula Yates, who died from a drug overdose in 2000 when Peaches Geldof was 11.
She was previously married to rock musician Max Drummey but the pair separated in 2009 after a six-month marriage.
Her career has included TV presenting, writing magazine columns and a short stint as a lingerie model.
She has two sisters - Fifi, 30, and 22-year-old Pixie - and a half-sister Tiger Lily, who is 16.
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