The two-time former U’s loanee drowned while swimming in the pool at his home in Athens last week.
His older brother James has been United’s club doctor since October 2020, and is taking time out away from his duties, while fellow elder brother Sam scored four goals in 11 games for the U’s before injury forced him to retire in September 2023.
Greek international George was playing for Panathinaikos, who he joined in May after seven years at Sheffield United.
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Vaulks said: “It’s a massive heartbreak for everyone here at the football club. Obviously, George’s brother is our doctor, and we send our sincere condolences to the family.
“I think the whole football community showed what a man he was, just from the messages I’ve read, and the people I know that knew him.
“We know his brother well, the doc, and we just want to send all our love to them really. I don’t have the words for someone going through that, but we’re all there with them.”