Representatives for the screen star confirmed on Saturday that she had welcomed the new arrival on 8 January.
"Mother and baby are happy and healthy," Laura's agent told PEOPLE Magazine.
Laura, who turns 50 next month, and her real estate agent husband Marc Schauer have chosen to name their baby boy Bennett Armistead Schauer.
The Love Actually actress managed to keep news of her pregnancy a secret until Bennett was born and has not been photographed in public since June 2013.
New York-born Laura married Colorado-born Marc in May 2009 after a three-year engagement.
The couple were as private about their nuptials as they have been about their first child, with Laura's representative simply saying "they are very happy" at the time.
Reports later emerged that Laura's close friend and fellow actor Liam Neeson had walked her down the aisle.