The Germany international joined the Gunners from Real Madrid for a club-record £42 million in the summer.
Ozil, who missed a penalty during Arsenal’s 2-0 Champions League defeat of Marseille on Tuesday, is still adjusting to life in England, but Gibbs feels the club are capable of winning their first trophy since 2005 following his arrival.
Gibbs told the Daily Mirror: “Mesut Ozil has raised the club, raised the dressing room.
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“It’s still really early, but I think everyone can see that there’s something special that we can do.
“A trophy is the objective, obviously. But a lot of the trophy competitions domestically haven’t really started.
“But we know we want to win something this season – it’s really important and we feel we can do it. There’s a lot of confidence in the dressing room and in the squad."
Gibbs has established himself as Arsenal’s first-choice left-back this season, despite the arrival of Nacho Monreal in January.
However, the England international revealed that he had never even played in the position until his Arsenal debut against Sheffield United in 2007.
“Literally, my first ever game at left-back was for the first team,” he said. “I’d never played there before. I still don’t really know how it came about! I was told the day before because we had a few injuries.
“It was in the Carling Cup. I didn’t have too much time to think about it. We won 3-0 and it was after that the manager said he wanted me to play there from now on.”