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Welbeck marked his first start in eight months with a brace as the Gunners beat Southampton 5-0 on Saturday to reach the fifth round of the FA Cup.
The former Manchester United striker, 26, missed much of last season through injury and only returned to action this January following another setback.
"He's worked very hard," said Wenger.
"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.
"I wondered if he be solid enough mentally to cope with that. But he became even more resilient and worked even harder."
Welbeck was making only his fourth appearance of the season against Southampton after suffering knee cartilage damage in a 2-2 draw with Manchester City on 8 May last year.
He looked sharp from the outset and put Arsenal in control with two cool finishes inside the first 22 minutes.
Welbeck then set up Arsenal's third with a cutback for Walcott, who scored a hat-trick.
"It was good to see Welbeck be so convincing," added Wenger.
"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.
"There are always two fears: the first is that it takes him too long with decision-making, and second that he would be scared for contact.
"But the runs and also fighting the defenders, it was important for me."
Welbeck has made 38 appearances for Arsenal since signing from Manchester United in September 2014.
Arsenal boss Arsene Wenger had feared Danny Welbeck would lose his edge after spending almost two years fighting knee injuries.