Welbeck, 23, secured a deadline day move to the Gunners, ending a 15-year affiliation with the Red Devils to move to London for a reported £16m.
Ferdinand feels that United sold a "top player" that will "flourish" in his new surroundings and go on to take English football by storm.
"I cannot believe United let Danny go, especially to Arsenal," Ferdinand 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.
"That will be good news for England, too, because if he is playing regularly that has to benefit the national team. 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. At Arsenal he will be the main man and I have no doubt he will flourish."
Welbeck is expected to make Arsenal his debut against United's local rivals Manchester City, who travel to the Emirates Stadium on Saturday.