The `Inception` star and her French actor-director partner Guillaume Canet became parents to a son on 19.05.11 who they have named Marcel.
A source revealed: "Mother and baby are fine."
The 35-year-old Oscar-winning actress - who gave birth in Paris - and Guillaume, 38, are also said to be "very happy" with the new arrival.
No other details about the tot or the delivery were available at the time of writing.
The couple first met when they starred alongside each other in 2003 movie `Love Me If You Dare` but only started dating in 2007.
Marion recently admitted she loved her life as an actress because she gets to live out her dreams.
The French star - who was the first person to receive an Oscar for a foreign language performance when she won the Best Actress accolade for her role in 2007`s `La Vie En Rose` - said: "I live as a girl who had big dreams and who is lucky enough to live those dreams while continuing to dream - while at the same time living a real life.
"I don`t want to be someone else. And I`m not going to let my job take me away from myself. I`m not going to be haunted or disturbed."