Five goals in his last six games and a number of assists suggests that Giroud, 26, is finally getting to grips with life in England.
Wenger said: "He still has some work to do but he convinces you about something more than just his game.
"It's his overall attitude. He is a fighter, he is ready to have a go and he is genuine.
"You don't cheat people on that, people smell that in the stands.
"That's why I feel he is accepted, not just because of his game but he is really genuinely committed on the pitch.
"He has the characteristics of a centre-forward I like in England - complete commitment, capability to win balls in the air and fighting attitude."