The 24-year-old Germany midfielder was a £42.4m recruit from Real Madrid on transfer deadline day.
"It is very physical here but I am really glad to play in the best league in the world."
Asked on Thursday if he thought the Gunners could challenge for the title, he responded: "Of course.
"I know the team, I know that talent we have here and I think every player wants to be successful. It will be difficult because this is the strongest league in the world."
Ozil, who is Arsenal's record signing, could feature for his new team when they face Sunderland at the Stadium of Light on Saturday.
"I have watched a lot of Premier League games," he said. "It is very physical here but I am really glad to play in the best league in the world.
"I want to prove myself in England and I look forward to playing here. I know I will prove myself here."
He added: "We want to play offensive and good football. To keep clean sheets and play attractive football.
"I can't promise to win trophies but I can promise as a team we will give our all to achieve this."
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