Welbeck has been injury-ridden over the last two years, spending a total of 20 months on the sidelines due to two knee-ligament problems.
The England frontman had only just returned from a serious knee injury when he suffered the same problem last May, which ruled him out of the summer’s European Championships.
But after being included in the starting XI for Arsenal’s FA Cup fourth-round tie at Southampton, Welbeck demonstrated his recovery by netting a brace in a 5-0 win.
“I wondered first of all would he be solid enough mentally to cope with that,” admitted Wenger.
“Then, secondly you hope he will go well after he comes back after the second surgery.
“He worked very hard, he went through some moments of very deep disappointment. Because when he had the setback and he had to go in again, as a professional player that’s very difficult.
“But he became even more resilient and worked even harder. He’s highly respected inside the club because he’s shown so much dedication.
“It was good to see Welbeck be so convincing. I didn’t expect him at that level, because I knew he worked very hard but I didn’t know how much efficiency it would be in a competitive game.
“It was great to see he hasn’t lost his runs or his finishing; it shows as well when you are able to transform that frustration in not playing into efficiency that he’s a special guy.”