The Costa Rica international was in fine form in Saturday’s 3-0 win at Swansea and scored his first Arsenal goal with a calm finish.
Wenger believes Campbell’s strike was important for his confidence, having had limited game time since his return to the club.
“I think he wanted to go (in the summer) because he didn’t play, which you can understand and as well because he didn’t play at all,” he said.
“Sometimes people want you to buy more and more players but after a while you have to look at your own players.
“He comes from Costa Rica, to get out of there and to come to (England) and to go to different leagues and survive, you need some character and he has shown that again today. In our job, all you can do is be ready and when you get your chance, take it and I think he did.
“When he came back he was on the waiting list and finally he got the chance and I’m very happy for him.
“I think he worked very hard, defended very well, created chances in the first half – he had that shot that was not that far off. He had another shot and in the second half he scored a goal and on top of that he worked very hard.”
Arsène Wenger added that he always knew that Joel Campbell had the attributes to succeed at Arsenal.
Meanwhile, Campbell has also expressed his joy at scoring his first goal for the club.
“I’m very happy,” he told Arsenal Player. “I had to wait for this moment and now we have to keep working to strengthen our team.
“I’m very happy but the important thing is the team wins. We had a good game so we have to keep going and prepare for the next game against Bayern Munich.
“The fans were incredible. They supported us the whole game and it was very important for us.”
The sweet away victory also saw Olivier Giroud scoring Arsenal’s 2,000th goal under Arsène Wenger.
The striker struck the opener in Saturday’s 3-0 win at Swansea to continue his fine run of six goals in as many games for club and country.
Arsenal now head to Munich on Wednesday to take on the German Champions, Bayern Munich at the Allianz Arena in the Champions League.
Arsène Wenger’s side became the first team to beat Bayern Munich since the German Super Cup when winning their Champions League Group F fixture 2-0 at Emirates Stadium recently.