And they didn't have to wait long – just days after the birth, the proud new mummy posted a snap of the newborn on Twitter.
In the picture, a radiant looking Dannii and her partner Kris Smith sit on a bed with Ethan between them, snoozing in a baby carrier.
And he's also sleeping soundly in a second close up shot, posted by Kris, who said: "Hey guys, first look at our beautiful Ethan, he is the most adorable little man, looks like his amazing mum."
Accompanying her snap, Danni posted the following message: "Hey everyone thanks for all your wishes, we are loving baby Ethan and Kris is the best dad in the world. X."
The 38-year-old gave birth on Monday in Melbourne's Royal Women's Hospital with her 32-year-old model boyfriend at her side.
It was reported that she had originally gone ahead with a home birth, but was rushed to hospital after suffering complications.
She was checked in under an alias to conceal her identity and protect her privacy.
Among the celebrities congratulating Dannii was her X Factor protégé Alexandra Burke, who tweeted: "Congrats babe on your new baby boy! Hope all is well and I can't wait to see you soon. Big kiss xxx."
Dannii's sister Kylie also offered her congratulations over the micro-blogging site, calling the new arrival "beautiful" and "gorgeous". She'll meet her new nephew in person later this month when she arrives in Australia.