With the Dutch striker now at Manchester United, the pressure is on attacking summer recruits Giroud, Lukas Podolski and midfielder Santi Cazorla to bring goals to the side.
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"It takes time to adapt, and it is especially hard for attacking players, but I am optimistic that both Giroud and Podolski can be a success," he told the Sunday Mirror.
"I have seen Giroud playing in France and he has the qualities you need in England. He is strong and he has a good touch. He can be like Van Persie in my opinion.
"Podolski is very mobile around the pitch and he is a Germany international with many caps. They will adapt. Santi Cazorla is someone I know well. He has adjusted to England very quickly and the fans will love him."
Arsenal have once again lost some of their biggest stars with both Van Persie and Alex Song moving on, but Pires believes that the past few seasons have shown that they know how to adapt to losing key players.
He added: "This is a difficult time for Arsene Wenger. He has lost important players in the last year like Gael Clichy, Cesc Fabregas, Van Persie and Song.
"But he has lost players in the past and replaced them and I am sure he will do it again."