The photogenic pair welcomed a healthy little girl named Ella Betsi Janet, weighing six lbs, three oz, at 2.16am on Sunday in Los Angeles.
"Ella is very small and unbelievably beautiful," her overjoyed mum told us, before adding fondly that the smasher "hasn't got much hair yet".
One of the baby's middle names - Janet - is in honour of Alice's own mother, who passed away ten years ago this month.
Speaking of his hopes for a big family earlier this year – he had his eye on a brood of three – the handsome Welshman said he wanted a daughter born in August, the same month as Alice.
He reasoned that then "she would be this strong-headed, fun-loving young thing and it would be great to have two women with that kind of energy in the house".
Though the baby has missed her 35-year-old dad's deadline by a matter of weeks, it's unlikely that the couple, who have promised to create "an environment of love and happiness" for her, will mind.
It's not known how long the new parents will have to devote themselves exclusively to their little superheroine, though, since they're both pretty busy careerwise.
102 Dalmatians star Alice has a recurring role in Lost as the younger version of Eloise Hawking. Meanwhile Ioan will next be seen in Nick Moran's new drama The Kid, also starring Natascha McElhone and Rupert Friend.