Speaking at the launch of his new Miami MLS franchise on Monday, Beckham discussed his old club's dealings in the transfer window with the fervent excitement of a man who still keeps a very close eye on the team he supports.
The 42-year-old admitted: "I still can't believe it's happened, to be honest. When he's been part of a club as big as Arsenal and then he moves a few hours away up north to the biggest club, it's astonishing to see.
"We all wish him luck. I'm a Manchester United fan so I am excited about having someone of his talent wearing a Manchester United shirt - so it's exciting times for us."
The former Real Madrid midfielder also weighed in on Jose Mourinho's new contract - signed last week - which ties the Portuguese manager to the club until 2020, saying: "Of course he's the right fit for Manchester United.
"We're talking about Jose Mourinho. He's one of the best managers in the game. Manchester United has had success over the last 25 years because we have had stability that has run throughout our club. Sir Alex Ferguson - the amount of time he was manager of the team - that's why we were successful because we had stability that ran through the club and that's what we need going forward.
"Everyone is going to have their own opinion of [Mourinho] as a manager, him as a person, him as an individual. But is he the right person to lead Manchester United? Yes, of course he is."