Rossdale tweeted news of the birth and said Bowie and Flynn were their mothers' maiden names.
Apollo's brothers are five-year-old Zuma and Kingston, seven.
Rossdale, 48, is best known as the lead singer of the rock band Bush and Stefani, 44, is the lead vocalist of the band No Doubt, and has released two hit solo albums. She is also a fashion designer.
The couple met in the mid-1990s and were married in 2002.
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