The 25-year-old French striker believes that despite not having as many resources at their disposal, the club can still compete for the title with both Manchester teams this term
After arriving in the summer from Ligue 1 champions Montpellier, the France international saw the Dutchman leave to join rivals Manchester United shortly afterwards, and Giroud is keen to play down talk that he has merely been brought in to replace last season's PFA Player of the Year award winner.
"I am not here to replace Van Persie or to make people forget him," Giroud told The Daily Mirror.
"I am here to bring something different. I don't have the pretension of saying I will replace him because I have every respect for him as he had an enormous season last year.
"I wish him good luck for the future but I need to bring what I can bring without being pretentious to say I am here to replace him. That would be very bad.
"I feel ready. Absolutely ready to assume the responsibility and make people say ‘yes, we have Olivier’. That’s how it is. If I didn’t think that I would never get my chance.
"If you sign for a big club it’s to replace another striker who leaves or you come and sit on the bench and wait for some game-time or wait until a striker is less efficient, needs a breather or is injured.
"Unfortunately that’s how it is football. Now I have a chance as Robin left. So I will get more time to play and I need to assume the responsibility. In fact, I must.
"Because that is my chance and I have to take it. The ball is in my court and the show must go on."
Arsenal have failed to win a trophy for seven years and Giroud believes increased consistency is needed from the Gunners to bring success back to north London.
He added: "Of course the fans want to win a trophy badly, I know that. When you are a top-level sportsman you have to believe and want to be the best.
"For us to fight for the title we need to have the spirit of a group. It could seem banal but it is important.
"It’s what makes the essence of the team, the solidarity and unity of the group. We all have to be going in the same direction.
"I watched the Premier League a lot. Arsenal are capable of playing great matches but, on the other hand, some games can pass them by. We must gain in consistency.
"Maybe we don’t have the means of great clubs like Man United or City who can construct a team of great players. We will fight with our means and I am convinced we will have a beautiful season."
Arsene Wenger has also brought in Germany international Lukas Podolski this summer to play alongside Giroud, and the 25-year-old says he has already developed a good understanding with the former Koln man.