The France international recently confessed that he seriously considered quitting the Gunners during the summer due to a lack of regular playing time last season.
Everton boss Ronald Koeman was desperate to bring Giroud on board, and could still make an approach when the transfer window reopens, but the 31-year-old is happy with his decision to reject the Toffees.
"I was very close to signing for another English club, Everton," he told Canal Football. "But I made the best choice I think. I stayed because I have a certain attachment to the club, quite simply. I am content to have remained. I am well in my head and in my boots."
Giroud recently joined an elite band of players to have hit 100 goals in an Arsenal shirt when finding the net against BATE Borisov.