Noah, who is the first child of the couple, showed off long eyelashes and adorable chubby cheeks as he sucked on a pacifier and snoozed, bundled up in a blanket and with a knit, reported Us magazine.
The tot has a half-brother in 10-year-old Kassius, Green's son with ex-girlfriend Vanessa Marcil.
Fox, 26, had said in a recent interview that she would like to have more kids in the future.
"All I wanted to do my whole, whole life was have a baby and, now, I've finally done it. I just want to give Noah as much of myself as I can. And I want to have more kids. That is where my heart is," she had said.