The family was spotted arriving in Milan, Italy, via private jet and the Ocean's Eleven star was seen disembarking from the plane holding a baby carrier.
The couple often vacations in Lake Como, Italy, and have a home there.
It's clear the two are adjusting well to life as parents, with human rights lawyer's mother, Baria Alamuddin, telling People that the pair are already pros.
“Oh my God, they were so beautiful, so happy, so contented,” she said. “You just look at them and you feel like they’ve been a mother and father for their whole lives.”
Photo Credit: Twitter / @shivanui