The 31-year-old joined from Lorient in 2010 and signed a contract extension until 2020 in January.
The France international previously stopped short of ruling out a move to Marseille, but has now committed his future to the Gunners.
"I am just here to enjoy my job and give everything for the team," he said.
"When I first got here, I didn't think about how long I would stay at this club - but now I am starting my eighth season."
Koscielny, who has made over 200 appearances for Arsenal, added: "Arsene Wenger is a big [inspiration] for me. He bought me from France, has given me everything to help me play for Arsenal, and has helped me as a man too.
"I have a big [loyalty] to this club and to the boss too. I am happy to be here with him and to fight for him because he is a great person."
Arsenal, who are on a pre-season tour of Australia and China, have recruited France striker Alexandre Lacazette from Lyon for a club record £46.5m and the left-back Sead Kolasinac from Schalke so far this summer.
Arsenal centre-back Laurent Koscielny says he has no desire to leave the club amid reported interest from French side Marseille.