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The baby, which has been named Phoenix, was born
at 1842 at London's Portland Hospital.
Her husband, Jimmy Gulzar, said mother and daughter are doing fine.
"The birth went just smooth and she sends you all her love," he said.
The other three Spices issued a joint statement saying: "We are really proud of Melanie - it was true girl power. We are all Spice aunties now."
Sporty Spice, Mel C, added as she left the hospital: "She's beautiful, I am very proud."
She shouted "girl power" to the photographers and well-wishers gathered outside.
Melanie Brown, 23, was rushed to hospital from her home at Little Marlow, Buckinghamshire at about 0400 on Friday.
Fellow Spice Girls Melanie Chisholm and Emma Bunton were soon with her.
Ms Brown - otherwise known as Scary Spice - married Gulzar in a lavish ceremony in September 1998. They met while he was dancing on the Spiceworld tour last year.
Fellow Spice Girl Victoria Adams is also expecting
a child, due later this month, by her footballer boyfriend David Beckham.
The singer, who comes from Leeds, had said the baby's name would begin with a P. When she married Gulzar,they both had tattoos on their fingers with each of their initials, together with the letter P.
Bookmaker William Hill was swamped with bets last month on the baby being called Paris. The organisation stopped taking bets, fearing inside knowledge was being used. Brown - who has started using the name Mel G in recent months - worked up until Christmas promoting the Spice Girls' festive No 1, Goodbye. However, when they played the Royal Variety Performance in December the foursome were seated.
Before Christmas she had her first hit outside the Spice Girls, teaming up with US hip-hop star Missy Elliot for I Want You Back, which reached number one in the UK.
The Duchess of York gave birth to her daughters
Beatrice and Eugenie at the Portland Hospital in 1988 and 1990.