Ozil arrived at the Emirates Stadium from Real Madrid in a €50 million deal on transfer deadline day, smashing the Gunners' transfer record and appeasing fans who questioned the club's ambition.
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"He's really enjoying himself." Gibbs told Arsenal's official website. "He looks very determined and happy and he's a humble boy as well.
"Coming from a club like Real Madrid you would expect a player to come with a bigger head on their shoulders but he's very down to earth and he's passionate.
"It's positive for us and a signing like Ozil is going to push our squad forward because you don't want to let him down. You want to perform for him and he will take us to the next level."
Arsenal sit with Tottenham at the top of the Premier League after an impressive start to the season, and Gibbs is confident they have the quality and depth to be a genuine force this term.
"I think the team is just gelling," he added. "We've had a strong finish to last season and people could see the players really gel. I think that's happening this season at an earlier stage.
"I'm very excited about the quality of the squad and when we get more players back from injury I feel like we'll be a force. We need to keep focused and build on our run. I'm sure we can be contenders."