"I stayed because I have a certain attachment to the club, quite simply".
The France striker was heavily linked with Ronald Koeman's side over the summer, along with West Ham and Marseille.
"I was very close to signing for another English club, Everton", Giroud told Canal Football while away on global duty.
The Toffees targeted the 31-year-old French forward as their first-choice replacement for the outgoing Romelu Lukaku, who left for Manchester United in a £75m fee - only for the deal for Giroud to collapse in the final stages.
Despite this, The Sun say Arsenal are keen to sign Lookman during the January transfer window and have been given hope that the youngster would be willing to return to London.
"But I made the best choice I think".
Giroud has seen his game time diminish this season.
Giroud, who also turned down Marseille and Lyon this summer, would not rule out a return to France: "I have a lot of respect for Marseille, I was a fan for years".
Giroud has once again struggled for regular game time with the Gunners this season, but after Everton made a disappointing start to the new season and are struggling at the wrong end of the table, it seems the striker is happy with his decision. I didn't want to return to France.
Victory over Belarus will confirm passage to the Russia World Cup for Giroud and his worldwide team-mates, seeing them top the pile as Group A victors.