Ozil has been in excellent form since joining from Real Madrid in a deal rumoured to be worth £42.5million on transfer deadline day, and was instrumental in Arsenal's 3-1 home win over Stoke City on Sunday.
The Germany international provided all three assists for Arsene Wenger's men as they eased past Mark Hughes' side to go top of the table, taking his tally to four assists in his first two Premier League games.
Gibbs has been impressed with Ozil's early performances, and is confident he will improve Arsenal in the long-term.
"He's really enjoying himself. He looks very determined and happy and he's a humble boy as well," the 23-year-old told Arsenal's official website.
"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 have won their last seven games since losing 3-1 to Aston Villa on the opening day of the season, and Gibbs is excited by the depth of talent at Wenger's disposal.
"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."
