Arsene Wenger's men have not won the league since the 2003-04 campaign but Ozil, who arrived on transfer deadline day from Real Madrid, believes that they can end that run this term.
Speaking to the media for the first time since his reported £42.5million club-record move, the Germany international was in no doubt that his new club can compete for silverware.
When asked whether Arsenal were title contenders, Ozil said: "Of course.
"This is one of the biggest clubs in the world."
The 24-year-old acknowledged that he can still improve following a productive three years at the Bernabeu.
"I had a very good time in Madrid but I have made the next step, I'm in the strongest league in the world," he continued.
"Many young players came here and got better, and became some of the best players in the world.
"For me the most important thing is I have fun. We have a busy schedule and I'm looking forward to it."
Ozil complained of a lack of respect from former boss Carlo Ancelotti following his departure for the Emirates Stadium.
However, he feels confident that Wenger can bring the best out of him and help his side achieve success.
"It feels great, I feel very good here," he added. "I'm sure the boss will improve me and I'm proud to be part of the team.
"When I talked to Arsene on the phone he was full of respect and as a player I need the respect."
Ozil could feature in Arsenal's trip to Sunderland on Saturday.
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