The 59-year-old actor discussed his "fulfilling" life with Amal, 42, and their 3-year-old twins, daughter Ella and son Alexander, in an interview with CBS Sunday Morning.
Clooney and Amal married in September 2014. In the context of his new film The Midnight Sky, Clooney said having someone to care for in real life has changed his life.
"There is no question that having Amal in my life changed everything for me. No question," the star said. "It was the first time that everything that she did and everything about her was infinitely more important than anything about me."
"Then we had these two knuckleheads, and it is very fulfilling," he added. "It's something I ... didn't see coming."
Clooney said he and Amal didn't discuss marriage while they were dating. Clooney ended up proposing to Amal "out of the blue."
"It took her a long time to say 'yeah.' I was on my knee for, like, 20 minutes. I finally said, 'I feel like I'm going to throw my hip out,'" the actor said with a smile.
"We told that story to her parents and they're like, 'There's something wrong with his hip?'" he added.
Similarly, Clooney said he and Amal "never" talked about having kids. The couple were surprised to find out they were having twins.
"You do the ultrasound and they're like, 'You got a baby boy.' I was like, 'Baby boy! Fantastic.' Then they go, 'And you got another one there.' I was like, 'I was up for one,'" Clooney said.
"Again, I'm old. All of the sudden it's, like, two. Literally, it's hard to get me to not talk. I just stood there for 10 minutes just staring at this piece of paper. Two," he added. "I'm so glad they have each other."
In the Midnight Sky, Clooney plays Augustine Lofthouse, a lonely scientist in the Arctic.. The film follows Augustine as he races to stop Sully (Felicity Jones) and her team of astronauts from returning home from space to a mysterious global catastrophe. Augustine makes a perilous journey while accompanied by a young girl, Iris (Caoilinn Springall).
Netflix released a trailer for The Midnight Sky in October. The film, starring and directed by Clooney, premieres in select theaters and on Netflix Dec. 23.