Giroud had been strongly linked with a move away from the Gunners after struggling to hold down a regular starting role during the 2016-17 campaign.
The Frenchman is expected to play second fiddle to club-record signing Alexandre Lacazette this season, meanwhile, following the striker's big-money move to London earlier this summer.
Giroud came off the bench to score Arsenal's winner in their 4-3 victory over Leicester City in the Premier League on Friday night, however, and the 30-year-old has explained his reasons for snubbing a move away ahead of the new season.
"To be honest, there was something in my soul and in my heart which told me to stay," Giroud told reporters. "I have been hesitating because I am the most happy man when I play and I am on the pitch.
"I keep the faith and I still believe I can have an important part to play this season in the club. I feel good in my head and also physically. So I am 100% focused on the club project."
Everton and West Ham United have reportedly both tried to sign Giroud this summer.