The ex-Neighbours actress gave birth to her first child with hubby Nick Candy last week, with the property developer confirming the news to The Daily Telegraph.
The couple have named the tot Luka Violet Toni Candy, with the proud dad revealing they named her after his late father, Tony - who died six weeks before his granddaughter's birth.
Speaking to the newspaper at the Wonderland Ball held by the Reuben Foundation to raise money for Great Ormond Street Hospital, Nick explained: "She was born a few days ago.
"We have decided to call her Luka Violet Toni Candy. Her nickname will be LuLu, but, obviously, if she ever goes into business, LuLu Candy just doesn't quite work. My father's nickname was always TC."
When asked about Valance's absence, Candy explained: Holly is at home. We aren't having any help at the moment. Holly doesn't want any; she wants to do it all ourselves at this stage, but that might change - it has only been a few days."
He went on to add: "[Holly] 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.
"It is such a shame that dad died six weeks before Luka was born, but I had the best role model possible in him, so, hopefully, if I can be anything like the father he was to me, when it comes to raising Luka, we'll be on to a winner."