The couple has named the baby boy Hayes Alba Warren -- their third child after girls Haven and Honor.
After giving birth, the actress revealed that Hayes' two elder siblings are "already obsessed with him" and that she is "happy" with her "three kids" and "would not want more children".
Father Cash also posted a photo of his newborn and captioned the post: "Hayes Alba Warren: You sure know how to ring in the new year! You showed up a few days early but we couldn’t be any happier. Your Mamma is the strongest woman I know ... you’re so lucky to have her by your side. You have two amazing sisters who already adore you and I know you’ll be thankful to have them guide the way. On your first day of life, I promise to love you, to cherish you, and to provide you with a sandbox full of dreams to explore. Welcome to the family my sweet baby Hayes! 12/31/2017"