The Jurassic World star said she has been named Lyla Maria Schwarzenegger Pratt.
He shared the news on Instagram alongside an image appearing to show him, his wife and their newborn daughter clasping their hands together.
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He said: “We are beyond thrilled to announce the birth of our daughter, Lyla Maria Schwarzenegger Pratt.
“We couldn’t be happier.
“Both mom and baby are doing great.
“We are extremely blessed.”
(Ian West/PA)
Schwarzenegger, who is an author and the daughter of actor and politician Arnold, also shared the news on social media.
The pair tied the knot last year.
Pratt has a son named Jack from his previous marriage to actress Anna Faris.
