The 56-year-old actor and his wife, Amal Clooney, welcomed their twin babies, a boy and a girl, on Tuesday, ET can confirm.
"This morning Amal and George welcomed Ella and Alexander Clooney into their lives. Ella, Alexander and Amal are all healthy, happy and doing fine," the couple said in a statement. "George is sedated and should recover in a few days."
"I don't know how you fully digest [having two], but I'm excited," the first-time father said while at CinemaCon in Las Vegas. "It will be fun."
"My wife says I can't name them Casa and Amigos. That's the one thing I'm not allowed to do," he joked about naming their children after his tequila company.
Amal dressed her growing belly in a custom-made Atelier Versace black-and-white feathered gown.
The Clooneys had been keeping a low profile leading up to the birth, residing at their home in Sonning, England, a source recently told ET.
For more on their new family of four, watch below: