The Frenchman was Ligue 1's top scorer last term and believes that he will be able to translate that form to the Premier League with time.
He told Fifa.com: "I'm not too worried about it, because I've been scoring in training and I feel pretty comfortable being a part of this team.
"I've been freezing up a little bit just when I've been about to pull the trigger and that's exactly what happened in my first few matches for France.
|15/4||Olivier Giroud is 15/4 with Bet365 to score two or more goals in Arsenal v Southampton
"Even as a young boy, I dreamed of playing in the Premier League," Giroud added of his desire to become the next in a long line of French heroes at the club.
"Remember, there were several big-name French players doing well at Arsenal at the time, guys like Patrick Vieira, Sylvain Wiltord, Robert Pires, Thierry Henry, among others, and that made an impression on me.
"I'm very proud to follow in their footsteps and I hope to make my mark at the club as well. I really am pleased with my decision to come here."
Asked if the presence of fellow Frenchman Arsene Wenger influenced his decision to move to the Emirates Stadium, the striker agreed: "Yes, because he knows me and has confidence in me. Generally speaking, the French guys here help you to settle in pretty quickly – there are actually quite a lot of French-speaking players overall.
"There are lots of people you can count on if you need help with something. But you can't let that hold you back in terms of mixing with the others, and that suits me fine as I really want to improve my English and speak fluently, without having to think about what I’m about to say.
"Being at Arsenal will help me with my development and, with a manager like Arsene Wenger in charge, I'm definitely in good hands."
|"The support from the fans is amazing! They chant non-stop and I felt very honoured that they sang a song about me"
- Olivier Giroud
Giroud also hailed the support that he has witnessed in the Premier League, praising the intelligence of fans in English stadia.
"The atmosphere in the stadiums is pretty much what I was expecting," he explained. "The support from the fans is amazing! They chant non-stop and I felt very honoured that they even sang a little song about me when I arrived.
"On top of that, the fans are very knowledgeable. They applaud when you block a clearance, when you drop back to help in defence, or when you put in a strong tackle. It's actually a tremendous way of looking at the game."