Scholes and Beckham were part of the class of '92, along with Nicky Butt and Gary and Phil Neville, which delivered success to the club under the guidance of Sir Alex Ferguson, who announced he was quitting last week.
Scholes, who is also calling time on his career, told the Daily Mail: "It's a sad day but hopefully David is happy with what he's done."
He added: "From the start you knew the quality he had and the professionalism. His range of passing and his free-kicks were brilliant and that was no accident - he was out there practising all day long.
"That's our year finished now. I think there's only Ryan Giggs, who was a year older than us, still going as strong as ever."
Eric Harrison, who was youth team coach at United, first came into contact with Beckham aged 12.
He said: "There's nobody in the world when they see a boy at 12, who can say he's going to go to such great heights as David. But I saw a very talented player - one absolutely in love with football.
"The hard work was the catalyst. He never had a lot of pace but in terms of stamina, running and work-rate, he was probably one of the best I've worked with."