The actor and the human rights attorney have welcomed a daughter, Ella, and a son, Alexander, the Oscar winner's publicist confirmed to ABC News.
"This morning Amal and George welcomed Ella and Alexander Clooney into their lives. Ella, Alexander and Amal are all healthy, happy and doing fine," a rep for the actor said in a statement.
The rep added, jokingly: "George is sedated and should recover in a few days."
Earlier this year, George Clooney confirmed that he was going to be a first-time father.
"It's exciting," he said during an interview with a French television program, "Rencontres de Cinema." "We're really happy and really excited and it's going to be an adventure."