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The actor, 52, spoke during the 45th Kennedy Center Honors ceremony at The Kennedy Center on Sunday in Washington, D.C., paying tribute to Clooney, 61, who was being honored for lifetime artistic achievements along with Amy Grant, Gladys Knight, Tania León and the band U2.
During his remarks, Damon joked about having made "hits" and "bombs" with Clooney, and enjoying all the career ups and downs together. He also poked fun at Clooney's "movie-star looks."
"George, I know a lot of people think you have movie-star looks, but let's be honest, it takes a village to style the star. PEOPLE Magazine's Sexiest Man Alive — I've been there, those experts can transform anyone," said Damon, who was 2007's Sexiest Man Alive.
"I have worked with George on some of his biggest hits and some of his biggest bombs. We have received rave reviews together, we have been slaughtered by the critics together," continued Damon. "And I have loved every minute of it."
TIZIANA FABI/AFP via Getty George Clooney and Matt Damon in 2017
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"George, You are one of the most talented people I have ever met across multiple disciplines," added Damon. "And here's the thing, if you said to people that the George they worked with 20 years ago, that in two decades he'd have two Academy Awards, he'd be nominated for Oscars in six different categories, and we'd all be in black tie in this beautiful venue watching him receive the Kennedy Center Honor, absolutely none of us would have been surprised."
He continued, "George, your talent and intelligence is visible and apparent to everyone who was lucky enough to work closely with you. You have earned everything. And it's been a privilege to work with you on the hits and the misses. And it's a privilege to call you my friend."
Damon and Clooney have shared the screen in movies like Ocean's Eleven (2001), Ocean's Twelve (2004) and Ocean's Thirteen (2007), Syriana (2005) and The Monuments Men (2014). Clooney directed Damon in 2017's Suburbicon too.
Damon interviewed Clooney for Interview magazine last year, and Clooney asked whether they should make another Ocean's movie together. That franchise also starred Julia Roberts, Brad Pitt, Casey Affleck, Andy Garcia, Don Cheadle and more.
"So here's a question. Should we do another Ocean's film? It's all I get asked. I think we should. We'd have to do it in style, right?" said Clooney, as Damon replied, "Yeah, exactly." Clooney then joked of the years-later sequel: "We're all wetting ourselves, holding canes and things."