Arsenal splashed out in excess of £40million to bring Germany international Ozil to Emirates Stadium on deadline day after a previously quiet summer in the transfer market.
Many of Ozil's team-mates at Real were stunned by his departure after the world-record signing of Gareth Bale from Tottenham left him surplus to Carlo Ancelotti's requirements.
Gunners boss Arsene Wenger, though, made it clear Ozil would be integral to the club's 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 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."