Fox, 26, announced on Facebook that Noah Shannon Green was born Sep 27, thesun.co.uk reports. "I gave birth to our son... He is healthy, happy and perfect."
The couple, who married in 2010, had been away from the public eye for a long time.
Fox is a stepmother to Green's 10-year-old son Kassius, from his previous marriage with actress Vanessa Marcil.
Photos: Kareena Kapoor Khan and Aamir Khan at Mumbai airport
Photos: SRK, wife Gauri, Aishwarya Rai, Shweta Bachchan at Vogue Awards
Photos: Harbhajan Singh-Geeta Basra's TV outing with daughter Hinaya
Photos: Malaika Arora flaunts ripped jeans like a boss!
Photos: Vaani Kapoor, Kriti Sanon, Dia Mirza sizzle on the ramp