The Money Monster actor, 56, and British human rights lawyer, 39, welcomed a baby boy and girl on Tuesday, June 6.
"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 to Us. "George is sedated and should recover in a few days."
Us Weekly confirmed in February that the two were set to become first-time parents. "[He's] getting a little anxious about the babies' arrival," an insider told Us in May. "But he’s nervous and excited, in a good way!"
The Oscar winner opened up about their next chapter during an interview on French program Rencontres de Cinema in February. "We are really happy and really excited. It’s going to be an adventure," he said at the time. "We’ve embraced it with arms wide open."
As Us exclusively reported, the Clooneys renovated their 17th century manor in London for their children.
The couple got engaged in April 2014 after several months of dating. They tied the knot at the seven-star Aman Venice hotel on the Grand Canal in Venice, Italy, in September 2014.
Sign up now for the Us Weekly newsletter to get breaking celebrity news, hot pics and more delivered straight to your inbox!
For the latest celebrity entertainment, news and lifestyle videos, subscribe to Us Weekly’s YouTube Page!