The 23-year-old striker joined the Gunners on a five-year deal on transfer deadline day after being deemed surplus to requirements at Old Trafford by new manager Louis van Gaal.
And Moyes, who was sacked after less than a year in charge of United earlier this season, was surprised to see United sell the England international to one of their Premier League rivals.
“Danny Welbeck was great for us at Manchester United,” Moyes told BBC Sport.
“We played him in nearly all the big games and, more importantly, [he was] one of your own boys you bring through.
“There are not many young British players out there, so it was a bit of a surprise for me [that he was sold to Arsenal]. But whoever is in charge has to decide what route they choose.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news