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Stefani gave birth at Cedars-Sinai Medical Center in Los Angeles. Both mother and child are doing well, said her rep.
On Saturday, Rossdale told PEOPLE: "Gwen's doing great! She looks amazing and she's doing real good."
Asked how it feels to be a new father, Rossdale added, "It's great! I love it!"
Stefani had long been open about her desire to be a mom. "I'm hoping my children will save me from my vanity," she told PEOPLE in 2004.
One thing is for certain: The baby will be well-dressed.
In recent months, Stefani and Rossdale were spotted stocking up on baby goods at trendy London boutiques like Elias & Grace in the couple's Primrose Hill neighborhood. And Stefani, a successful fashion designer, has added clothes for babies and toddlers to her Harajuku Lovers line.
Stefani first announced her pregnancy last December during a concert in Ft. Lauderdale, Fla. "I want you to say it loud enough so the baby hears it," Stefani yelled to the audience during a sing-along on her song "Crash." The crowd went wild.
"This is the end of a huge chapter for me," Stefani added. A camera then cut to an audience member holding a hand-lettered poster that read: "Congrats on Baby."
Stefani, 36, and Rossdale, 40, married in September 2002 in two separate ceremonies: a London wedding at St. Paul's Church and Los Angeles nuptials two weeks later.
The pair began dating in 1995, when Stefani's band, No Doubt, toured as openers for Rossdale's then-group, Bush.
This is the first child for Stefani; Rossdale discovered in 2004 that he has a 16-year-old daughter, Daisy, with his ex, fashion designer Pearl Lowe.
