The couple, who got engaged in September 2013, announced their news last night (4 September) and have decided to call their daughter Rose.
Hollywood actress Scarlett and French former journalist Romain are a notoriously private pair and have said they wish to keep further details about their bundle of joy out of the spotlight.
The rep said in a statement released to The Associated Press that "mother and baby are doing well".
Their newborn daughter is Scarlett and Romain's first child together. Three months before her pregnancy was announced, Scarlett - who was previously married to Ryan Reynolds - had spoken about her desire to start a family.
"I would like to have my own family, that would be nice," she said in an interview. "They say it's never the right time and I am sure that's true, but I think you have to plan it like anything else."
Celebrities who have welcomed babies in 2014:
Copyright: Rex Features WENN/Matthew Taylor/Daniel Deme/Josiah True/Matthre Taylor/Joe