Van Persie joined Manchester United last week after eight years at the club but Giroud, a summer signing from Montpellier, has claimed that he is a different player to the Dutchman.
The French striker told The Sun: "I am not here to replace Van Persie or to make people forget him.
"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."
Giroud joined the Gunners for £13m after scoring 21 goals in Ligue 1 as Montpellier were crowned champions.