Arsenal had chased a number of strikers during the summer transfer window, but the France international has responded by bagging four Premier League goals in as many games.
The North Londoners attempted to sign the likes of Luis Suarez and Gonzalo Higuain during the transfer window, but those moves proved unsuccessful — leaving Giroud as the club's leading man.
The Frenchman has since been in excellent form this season, scoring in each of the Gunners' four Premier League games, and Wenger has been pleased with the manner of the 26-year-old's response.
"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," said Wenger ahead of Sunday's clash with Stoke. "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."