The US actress and her husband Marc Schauer welcomed a son, Bennet Armistead Schauer, on January 8. It is the first child for the couple.
“Mother and baby are happy and healthy,” Linney’s spokesperson told People magazine.
Linney, a three-time Oscar nominee who featured in the romantic ensemble film Love, Actually and was the star of the star of TV’s cancer comedy-drama The Big C, married Mr Schauer in 2009.
Linney did not announce her pregnancy and has stayed out of the public eye in recent months.
One of her last public appearances was at the 2013 Women In Film’s Crystal + Lucy Awards in Beverly Hills last June.