On Wednesday evening he shared a touching Instagram post.
The dad penned, "Last night at 10.15pm the world became a better place, the birth of our baby girl Mila Elle has been the most magical adventure ever."
He continued alongside his baby's first photo with the new mum, Smith continued, "@thisisme.sb was a rock and I can never repay her efforts to get our baby to us safe and sound."
"We couldn't have done it without the help of our midwife Sam and the nurse and staff at Royal North Shore public hospital."
"We love you all, thank you..."
Friends like Sam Wood and Sasha Mielczarek were quick to congratulate the pair.
Minogue, who shares Ethan with the new dad, told WHO, "I am so excited for the both of them. I could not be more happy."