The former pop singer and Strictly Come Dancing star, 30, and her husband, Nick Candy, welcomed their new daughter a few days ago.
Property developer Nick, 40, confirmed the good news to the The Sunday Telegraph.
"She was born a few days ago," Nick said. "We have decided to call her Luka Violet Toni Candy. Her nickname will be LuLu."
He added: "She is a perfect mother. It was a natural birth. She is from a big Australian family, with younger siblings, so she knows exactly what she is doing."
Nick also revealed that the couple aren't going to "have any help".
Former Neighbours actress Holly was last seen at the launch of the autumn/winter 2013 edition of Candy magazine at London's Saatchi Gallery in October.
She wore a black and white striped dress, which camouflaged her baby bump.
Holly wed Nick in an extravagant £3million ceremony in Los Angeles last year.
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