According to reports, the baby was actually born two weeks ago, but the very private couple kept the birth a secret. No word on a name or whether the child is a boy or a girl.
Cooper, 42, and Shayk, 31, have been together since 2015.
Cooper was married to actress Jennifer Esposito in 2006, but divorced a year later. Shayk has never been married but was in a long-term relationship with soccer star Cristiano Ronaldo before dating Cooper.
After reports of the birth surfaced, Ellen DeGeneres congratulated the couple on Twitter.
Congrats Irina Shayk and Bradley Cooper on your baby! Bradley, you're going to be a wonderful dad. Just don't take the baby to Vegas.— Ellen DeGeneres (@TheEllenShow) April 9, 2017