Peaches Geldof spent her first few days as a new mum worried sick after her newborn son was whisked away to an intensive care unit as he struggled to breathe.
Little Astala was rushed off for emergency treatment just moments after his dad Thomas Cohen snipped his umbilical cord.
Peaches admits she was terror-stricken and longed to hold her baby, who was delivered via Caesarean section last month.
She told Hello! magazine: "He had a lack of something called surfactant, which made it a struggle for him to breathe. He was in intensive care for a few days....
"It was the most terrifying experience to have our tiny baby whisked away like that. I was yearning for that skin-to-skin contact I'd waited so long for and to not be able to hold him and nurse him and comfort him was so upsetting."
The new mum was brought to tears when she was finally united with her little boy, who has since made a full recovery.
She added: "To be able to finally hold him and take in all his little features was wonderful."
Peaches isn't the only one thrilled with the new arrival - her dad Bob Geldof is "besotted" with Astala, although he is still coming to grips with his unusual name.
Recalling the rocker's first encounter with his grandson, she said: "He was incredibly gentle with Astala; he took him aside and was so quiet, which isn't something my dad's renowned for... He's besotted with Astala because he's his first grandchild but especially, I think, because he's the first boy in the family."
The full story appears in this week's issue of Hello! Magazine: