According to a birth certificate, the 'Teenage Mutant Ninja Turtles' star gave birth to Bodhi on February 12, reported Us magzine.
The moniker Bodhi means 'awakened' in Buddhism and can sometimes be translated to 'enlightenment' in English.
Fox, 27, and Green, 40, who wed in June 2010, are already parents to son Noah, 17 months.
The couple had announced that they were expecting their second child together last August. At the time, Fox was busy filming 2014's 'Teenage Mutant Ninja Turtles' in New York City.