The couple named their daughter Lea de Seine Shayk Cooper, reported E! Online.
"They are both extremely thrilled and feel so blessed," a source said.
Lea is the first child for the 31-year-old Russian supermodel and the "Silver Linings Playbook" actor, who have been dating since spring 2015.
Shayk's pregnancy news came out in November after she showcased a baby bump while walking the runway at the 2016 Victoria's Secret Fashion Show.
The two were first romantically linked in May 2015 when they were spotted kissing in New York City.