The 26-year-old Frenchman saw his future at the club in some doubt prior to the start of the 2013-14 campaign as a number of high-profile strikers, including Gonzalo Higuain and Luis Suarez, were linked with Arsenal.
Giroud, though, continued to train hard and has been rewarded with a flurry of goals in the opening month of the new season, scoring in each of Arsenal's four Premier League games.
Wenger has praised Giroud ahead of Sunday's clash with Stoke City, as he 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."
Arsenal entertain Stoke striving for their seventh win in a row in all competitions and Wenger is boosted by the return to training of Mikel Arteta.
The 31-year-old midfielder has failed to make an appearance in the new campaign after struggling with a quadricep injury.
He added: "He is back in full training (and) a decision will be made (on Saturday).
"He is a leader - we are happy to have him back."
