The X Factor judge, 38, gave birth to her son at the Royal Women's Hospital in Melbourne, Australia, yesterday.
Dannii and Kris, 31, have named him Ethan Edward Smith.
'Kris Smith and Dannii Minogue are thrilled to announce the arrival of Ethan Edward Smith on 5th July 2010,' reads a statement from manager Melissa Le Gear.
'Mother and baby are doing well and dad is very proud. They request their privacy at this special time to adjust as new parents.'
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