The baby is called Joshua and a spokesperson said mother and baby were "both doing very well".
Joshua's dad, former Westlife bouncer Fran Cosgrove, was with 20-year-old Natasha when she gave birth.
The couple decided to name their son after Natasha's granddad George's nickname.
Original member Kerry Katona is also a mum, but unlike her, Natasha isn't thinking of quitting the band.
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