The United youth product left for the Emirates Stadium in a £16 million deal on transfer deadline day as Radamel Falcao arrived on loan from Monaco.
Welbeck had reportedly been told by new manager Louis van Gaal that he would be allowed to leave as he entered the final two years of his contract.
But Ferdinand, who departed Old Trafford for QPR during the close-season, was left struggling to comprehend the decision to let the England international move on.
"I cannot believe United let Danny go, especially to Arsenal," he told The Sun. "That seems mad to me.
"He's a real threat to defenders and, if Arsenal use him right, he will be very dangerous for them.
"Danny has everything to be a top player. English football has yet to see what he can really do because he hasn't been getting a run of games.
"I think he felt frustrated at United because, even if he did well, Robin van Persie and Wayne Rooney would be ahead of him."
Although Ferdinand was disappointed by Welbeck's sale, he believes Arsenal have pulled off something of a coup in securing the 23-year-old's services.
"At Arsenal, he will be the main man and I have no doubt he will flourish," Ferdinand added.
"Imagine the pace Arsenal will have when everyone is fit. There will be Alex Oxlade-Chamberlain with three fliers in front of him in Theo Walcott, Alexis Sanchez and Danny.
"I'm telling you they would give Usain Bolt's Jamaican 4x100m team a run for their money."
Welbeck scored nine Premier League goals in the 2013-14 season before featuring twice for his country at the World Cup in Brazil.
