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 integral part 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.
"The quality is very high in this team and at this club, that is the most important thing, to have players of quality because that makes a difference," said Flamini - who left Arsenal in 2008 after running down his contract - on the club's official website.
"The team spirit is also very good, and we saw on Sunday (against Tottenham) that everyone was helping each other on the pitch, that makes a difference in the big games."
Ozil's signing has proved hugely popular with Arsenal supporters, and a survey by online retailers UKSoccershop.com revealed his shirt sales were outstripping those of Bale by five to one.
Arsenal - now owned outright by American tycoon Stan Kroenke - have long championed their self-sustaining business model, powered by the additional revenue from their 60,000-seater stadium at Ashburton Grove.
Chief commercial officer Tom Fox maintains it is an ethos which will mean when some silverware finally arrives, it will be all the sweeter.
Gibbs has had a good start to the new season, scoring against Fenerbahce in the Champions League play-off
In an interview with Marketing Week, Fox said: "When we win, we will win on the back of our own effort, on the back of our own hard work and revenue that we as a club generate based on our power as a global brand.
"We won't win on the back of a wealthy benefactor reaching into his pocket and solving the problem that way."
Fox continued: "We believe, and I think our fans believe, that success earned in the way that we are going about it, in a very difficult landscape and a very challenging business, is the sweeter victory.
"We don't exist for commercial purposes, we exist as a football club, to play football matches, to win and to make our fans feel proud."