The actress, 40, is pregnant with her third child, her rep confirms to PEOPLE.
Connelly and The Tourist star Bettany, 39, are already parents to son Stellan, 7, as well as Kai, 13, from her previous relationship with David Dugan.
"Becoming a mother has made all the difference in terms of learning to take more responsibility for myself and my life," she has said.
"Parenthood changed the way I do everything. The biggest thing for me is wanting my kids to grow up safely and have happy lives. To me, that's enough."
The couple, who met filming A Beautiful Mind, wed in Scotland in 2003.
Reporting by BLAINE ZUCKERMAN