UsMagazine.com said Agnes Lark Bettany was born via scheduled home water birth May 31.
"Everyone is healthy and doing well," Connelly's representative told UsMagazine.com. "The family is very excited."
Connelly and Bettany, both 40, met on the 2001 film set of "A Beautiful Mind" and married in 2003. They are the parents of a 7-year-old son named Stellan.
Connelly also has a 13-year-old son from a previous relationship.
Celebrity Couples of 2014 [PHOTOS]