The new arrival, whose name is Luka Violet Toni, arrived "a few days ago" according to proud new dad Nick.
"Holly is a perfect mother," property millionaire Nick told The Sunday Telegraph. "It was a natural birth."
"We have decided to call her Luka Violet Toni Candy," he added. "Her nickname will be LuLu, but, if she ever goes into business, LuLu Candy doesn't quite work!"
Former Neighbours actress Holly kept a low profile during her pregnancy.
The 30-year-old proved she had mastered maternity fashion when she showed off her baby bump in a monochrome striped dress back in October.
The mum-to-be beamed for photographers as she arrived at a star-studded party at London's Saatchi Gallery.
News that Melbourne-born Holly and her husband were expecting a baby emerged when photos of Holly's bump were published by Australian magazine Women's Day.
Only a month after their lavish LA wedding, Holly and Nick revealed that were already thinking about starting a family together.
"Finally at 30 I am coming round to the idea of babies and Nick, at 40, is well and truly ready," revealed the Kiss Kiss singer. "I think he might just get his way. I can see it now: I will be the bad cop – the strict one – and he will be the fabulous, fun dad!"