The No Doubt singer, 44, gave birth to the baby boy, named Apollo, on Friday (28 February).
On Saturday, Gavin tweeted: "Welcome Apollo Bowie Flynn Rossdale."
He went on to explain that Bowie is his mother's maiden name and Flynn is the maiden name of Gwen's mother.
Gwen and the 48-year-old frontman of Bush have been married for 11 years. They are already parents to Kingston, seven, and Zuma, five. Gavin also has daughter Daisy, his child with ex-Pearl Lowe.
After months of speculation about her blossoming baby bump, Gwen finally admitted she was pregnant when she joined Instagram in January and announced she was expecting another boy.
The L.A.M.B designer said: "I was ready to hand over the crown. But I guess I am still queen of the house. #itsaboy #surroundedbyboys."
Celebrities including Gwyneth Paltrow, Jessica Alba and Nicole Richie attended Gwen's baby shower last month at Hotel Bel Air and bought blue-coloured gifts.
On 20 February, Gwen took to Twitter to express how she felt about the final few weeks of pregnancy...
She joked: "Somebody please pop me soon gx."
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