According to Elsa's mother Cristina, the couple are "overflowing with happiness", as she told HELLO! magazine's sister publication HOLA!.
She added: "Since the little one was born they can't take the smiles off their faces."
Cristina flew to Britain from Spain with Elsa's brother Christian to be there to welcome the new arrival. Chris' parents Craig and Leonie also flew in from Australia.
"It was a natural birth, and of course Chris was by her side," says the pretty actress' mum."Elsa has always wanted to be a mother and I'm sure she will be fantastic.
"Of the Thor star, she says: "Chris is the most loving and attentive father I have ever seen. He's a natural and he adores her."