Wenger admitted Giroud has had to endure a difficult summer amid speculation Arsenal would sign a striker to replace him.
Wenger said: "Every day when he opened a newspaper he saw another striker coming here but he didn't say anything. For me that's the best answer you can give when you're a football player. Don't talk too much, play and show how good you are. Many people forget that sometimes but that's the core of your job.
"I believe he has improved technically in his link play and that will come out throughout the season. He has a huge physical presence that is very difficult to find these days. This season is a big test for Olivier but I'm sure he will have a great season.
"He has a kind of positive mentality that comes out. He has a good self-esteem that is a very important quality because when you're a striker you have to deal with a lot of pressure. It doesn't affect him too much when he doesn't always score but, overall, I think he has a very strong mentality."