The 'Catch-22' star - who has 23-month-old twins Ella and Alexander with his lawyer wife Amal Clooney - quipped that it was "a little irritating" to share his birth date with the royal couple's son.
Speaking to 'Entertainment Tonight', he laughed: "It was a little irritating, because that kid really is stealing my thunder!"
This was my day! I was sharing it already with Orson Welles and Sigmund Freud!"
Joking aside, the silver fox is thrilled for the new parents - whose star-studded Windsor Castle wedding he and Amal attended last May - and gushed that they are "a lovely couple".
He said: "I'm very happy. They're a lovely couple, so it's very exciting."
George admitted that he doesn't feel it's his place to give Prince Harry and Duchess Meghan any parenting tips and made a joke about his age.
He said: "I don't give advice, I'm 58.
"At 58 you just go, 'Ugggh.' I just walk with a walker everywhere I go."
Meanwhile, it's believed the 37-year-old former actress - who was known as Meghan Markle before she married Prince Harry last May - and the flame-haired prince will share the first photograph of their son on Wednesday (08.05.18) as well as announce the name they have chosen for him.
The birth was officially announced in the forecourt of Buckingham Palace, in keeping with tradition.
The typewritten note - which was in a gold frame - simply stated: "The Queen and the Royal Family are delighted at the news that Her Royal Highness The Duchess of Sussex was safely delivered of a son at 05.26am today. Her Royal Highness and her child are both doing well."
Shortly after the couple confirmed their son had been born via Instagram, Harry, 34, spoke with reporters and hailed the birth as an "amazing experience."