Ozil, 24, completed a transfer-deadline switch from Real Madrid, in what is understood to be a £43million deal, to give manager Arsene Wenger the new top-level addition he has long craved.
Many of Ozil's team-mates at Madrid were stunned by his departure - the creative midfielder suddenly no longer central in the plans of manager Carlo Ancelotti following the world-record signing of Gareth Bale from Tottenham.
Wenger, though, made it clear Ozil would be integral to the Gunners' ambitions - and Gibbs believes his arrival can help all of the players raise their own games this season in the quest for a first trophy since 2005.
"It is a statement to what the club want to do and what the club want to achieve," Gibbs said on Arsenal Player.
"It is something that everyone has been waiting for so now we have a big signing to help push us to the next level. He has got a clinical side to him and technically he is world-class.
"He is going to create a lot of problems for opposition we come up against and hopefully he can continue the form that he had with Real Madrid."
Signing Ozil proved to be Wenger's masterstroke in an otherwise rather flat transfer window, with the free signings of Yaya Sanogo and Mathieu Flamini the only other additions before a loan move for Palermo goalkeeper Emiliano Viviano was pushed through on deadline day.
Midfielder Flamini made his second Arsenal debut in a 1-0 league win over Tottenham before the international break, having rejoined his former club after being released by AC Milan.
The 29-year-old - who was an important member of the side which reached the 2006 Champions League final - is in no doubt the squad have enough strength in depth to mount a sustained challenge for honours.