The 39-year-old human rights lawyer and 56-year-old Hollywood star tied the knot in Venice in 2014
"This morning Amal and George welcomed Ella and Alexander Clooney into their lives," Stan Rosenfeld said on behalf of the couple. "Ella, Alexander and Amal are all healthy, happy and doing fine."
"George is sedated and should recover in a few days."
The 39-year-old human rights lawyer and 56-year-old Hollywood star - both first-time parents - tied the knot in Venice in 2014.