The German international midfielder joined the Gunners from Real Madrid for a club-record fee of £42.5m on transfer deadline day.
"It is a statement to what the club want to do and what the club want to achieve," Gibbs told Arsenal's official website.
"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 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."
Arsenal return to Premier League action on Saturday with a trip to Sunderland.