The Germany international moved from Real Madrid to Emirates Stadium on transfer deadline day and could be involved as soon as Saturday when Arsène Wenger's side travel to Sunderland in the Premier League.
Gibbs believes Ozil's arrival echoes that of Dennis Bergkamp, whose signing in 1995 helped spark a long period of success for Arsenal.
He's going to create a lot of problems for opposition we come up against
"I'm very excited, when a world-class player comes in and joins you've got to be excited," Gibbs told Arsenal Player.
"I'm sure he'll settle in quickly because we've got Lukas [Podolski] and Per [Mertesacker] with him to get him settled so it shouldn't take him too long. I'm really looking forward to working with him.
"He's got a clinical side to him and technically he's world-class. He's 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.
"He'll still have work to do to match Dennis Bergkamp and what he's done for the Club. But he's a world-class player and he looks very determined to come and help the team out.
"It's a statement to what the Club want to do and what the Club want to achieve. It's something that everyone's been waiting for so now we have a big signing to help push us to the next level."