"Listen, I'm scared to death, it's terrifying. You're afraid of breaking them. They're so little," he said as reported by People Magazine.
The 56-yearo-old added he and wife Amal Clooney have been sharing their babies' milestones, including changing diapers.
"It's like cleaning up your dog's poop."
The first-time father also revealed his children have recently been introduced to solid food.
He explained: "We introduced the children to solid food on Friday. How that goes in as a carrot and how that comes out the way it comes out is shocking. I don't know what's going from here to here. What happens?"
The couple welcomed their twins in June. (ANI)