Katherine’s brother, Patrick Schwarzenegger, confirmed the news on Sunday.
Speaking to Entertainment Tonight, the actor said: “They’re doing great, just got her a little gift.”
He then showed the camera a package wrapped with a pink ribbon. However, he did not confirm the baby’s gender.
The new arrival is Katherine’s first child but Chris already has a seven-year-old son, called Jack, with his ex-wife actor Anna Faris.
News that the couple were expecting their first child together hit headlines in April, just 10 months after they got married.
The couple's pregnancy was confirmed by Katherine’s mother, Maria Shriver, when Chris appeared as a guest on her Instagram Live series #HomeTogether.
“You're gonna have another beautiful family member,” Maria said to Chris at the time.
The couple kept the pregnancy largely under wraps, with Chris only recently publicly addressing the news on Twitter when his wife was nearing her due date.
Sharing a tweet about Katherine’s podcast, he wrote: “So proud of my darling for her amazing podcast. Nine months pregnant, in quarantine and still working her butt off. Check it out. Based on her NY Times best-selling book! I’m a lucky lucky man.”
Days prior to the birth of their newborn, the Jurassic World star also shared a photo on Instagram stories of himself and his pregnant wife alongside the caption: “Ready to pop, still don't stop.”
In the photo, Katherine looked heavily pregnant in a black tank top and leggings as she posed alongside her husband.
Speaking about his daughter’s pregnancy during an appearance on the Tonight Show Starring Jimmy Fallon, the 72-year-old said: “Can you believe that? That is really exciting news that Katherine now [to] be pregnant and have a baby—I don’t know when exactly, but sometime this summer.
“And, inevitably, I’m really looking forward to playing around with whatever it is, she or he, and have some fun. This is a unique experience.”
Watch the latest ‘The Baby Bump with Lauren Pope’ videos from Yahoo UK