The X Factor judge gave birth in Melbourne on Monday 5 July, but managed to keep the good news a secret for two days. Boyfriend Kris Smith was at her side.
Big sister Kylie spent Monday in Ibiza promoting her new album, Aphrodite, but is expected to fly home in the next week to meet her new nephew.
Dannii has been based in Australia for several months in preparation for the birth, but right up until the last minute she was writing on her Twitter page how much she is missing Britain. "Looking forward to catching up on X Factor auditions. Can’t wait to see Simon, Cheryl and Louis again soon – miss them very much."
The birth came just a week after the couple moved into their new £1 million mansion in Melbourne.