Johansson gave birth to Rose Dorothy in New York City, and the newborn's middle name is apparently a homage to the actress's late grandmother, according to People magazine.
A spokesperson for the happy couple released a statement confirming the mother and child are doing well.
"The couple is seeking privacy and are supporters of the No Kids Policy, the celebrity effort to keep famous folks' children out of the public eye."
The 29 year-old star's pregnancy news broke in March this year, which came only six months after Johansson announced that she and Dauriac, who is a French journalist, became engaged to be married.