The husband-and-wife team were snapped taking their litlle one for a walk in London, where she was born.
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Elsa gave birth on May 11 in the British capital where Chris was busy filming.
The couple are "overflowing with happiness", Elsa's mother Cristina tells HELLO! magazine's sister publication HOLA!, adding: "Since the little one was born they can't take the smiles off their faces."
Cristina flew to England 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 Elsa's mum.
"Elsa has always wanted to be a mother and I'm sure she will be fantastic."
Of the Troy actor, she says: "Chris is the most loving and attentive father I have ever seen. He's a natural and he adores her."
The couple chose her name, "because Chris had always like the name Indi or Indiana for a boy, and by chance, Elsa really liked the name India for a girl".
"So it was left to fate to decide if the name would be for a girl or boy… in the end it was India."
They added Rose: "Because, curiously, both Chris and Elsa both had grandmothers called Rose."