The Frenchman has found himself under immense pressure to replace Robin van Persie at the Emirates Stadium and had to wait until October to register his first Premier League goal for the Gunners.
However, Parlour has defended the 26-year-old and firmly believes that Giroud will be a hit at Arsenal.
"It does take time to settle at a new club and maybe into a new way of life for his family. Some players settle straight away and others take a little bit more time but I think he has done ok," Parlour told talkSPORT.
"He had a brilliant game against West Ham. I think Giroud is the main man [at Arsenal]. The goal against West Ham will help him to push on now.
"I think he will be a really good signing."
Giroud joined Arsenal from Montpellier HSC in the Summer.