Speaking with ET's Nancy O'Dell at the premiere of his upcoming Hulu dramedy Catch-22 in Hollywood on Tuesday, Clooney laughingly addressed the regal birth, and how it affected his own special day.
"It was a little irritating, because that kid really is stealing my thunder!" Clooney joked. "This was my day! I was sharing it already with Orson Welles and Sigmund Freud!"
Clooney and the as-of-yet unnamed royal baby also share their birthday with rapper Meek Mill, Dancing With the Stars host Tom Bergeron, former U.K. Prime Minister Tony Blair, silent film star Rudolph Valentino, NBA all-star Chris Paul and singer-songwriter Bob Seger.
While Clooney feigned disappointment over sharing the b-day attention, the actor -- who was one of the celeb guests as the Royal wedding when the Duke and Duchess of Sussex tied the knot almost a year ago -- said he was overjoyed for the new parents.
"I'm very happy. They're a lovely couple, so it's very exciting," Clooney marveled.
Earlier in the evening, Clooney sat down on Jimmy Kimmel Live! where he also addressed the royal baby, and shut down wild rumors that the new parents would turn to him to be their baby's god father.
"That would be a bad idea," Clooney deadpanned. "I shouldn't be the god father. I'm a father of twins and I can barely do that!"
""I should not be anyone's god father!" he added with a laugh.
However, despite having two children of his own -- 1-year-old twins Alex and Ella, whom he shares with wife Amal Clooney -- Clooney told ET on the red carpet that he doesn't feel it's his place to give the Duke and Duchess, or anyone else for that matter, advice on anything.
"I don't give advice, I'm 58," he quipped. "At 58 you just go, 'Ugggh.' I just walk with a walker everywhere I go."
While Clooney may joke about slowing down now that he's in his late 50s, there's certainly no sign of that when it comes to his career. Especially with his new Hulu series Catch-22, on which he serves as an executive producer, director and star.
Explaining what drew him to the project in such a big capacity, Clooney explained, "I thought it was a really good script and I thought it was a really good time."
"I think it's always a really good time to talk about the absurdity of war," he added. "I don't think that ever gets old."
While satires about the morality of military action and combat may interest a certain demographic, Clooney also joked that he wanted to broaden the show's appeal so he made sure to include a lot of "male nudity" and shirtless men.
"What happens is, no one asks me to take my shirt off anymore, so I made them take their shirts off!" Clooney said with faux-indignation in his voice.
Whether you're interested in a searing dark comedy about the surreal absurdity of combat or just want to see shirtless men, fans can catch Clooney's new series Catch-22 when it premieres on Hulu on May 17.