It's the first baby for Jennifer and her husband, British actress Paul Bettany, but Agnes joins Jennifer's older children, sons Kai, 13, and Stellan, seven, from a previous relationship.
The new arrival was born at home in a birthing pool, and mum and baby are said to be 'doing well'.
''Everyone is healthy and doing well,' Jennifer's spokesperson announced to Us magazine. 'The family is very excited.'
While we quite like Anges, we're not too sure on Lark as a second name - should Jennifer and Paul be put in our unusual celeb baby names gallery?