The 24-year-old was introduced to the media on Thursday, having been on international duty with his country since his club-record move to The Emirates on deadline day.
Ozil, who joined the Gunners for £42.5million from Real Madrid, scored a penalty in Germany's 3-0 win over the Faroe Islands on Tuesday and is expected to make his Premier League debut at Sunderland this Saturday.
Arsenal have begun their Premier League campaign with two victories and one defeat, and Ozil is confident they have the quality to be title contenders.
Asked if Arsenal can challenge for the title, he said: "Of course, definitely. I know the team and the talent we have here. Every player wants to be successful and Arsenal are one of the biggest clubs in the world.
"We definitely want to achieve something with this team - that is what we work for. Of course it will be very difficult because the league is the strongest in the world. But we will give everything to achieve success.
"We want to play attractive football to improve but of course also successful football. I can't promise to win trophies but I can promise as a team we can give our all to in trophies."
Ozil said that he consulted his international team-mates, Lukas Podolski and Per Mertesacker, about the club - but his central reason for signing for the Gunners was Arsene Wenger.
"Arsenal is a very well-known club, a very successful club with very young players, and the young players develop very well here," Ozil said.
"This was one of the reasons why I chose to come here, I want to continue to improve myself.
"I am really happy to be here under such a great manager.
"That was most important for us, what he (Wenger) thinks about me, what his plans are with me. I decided to come to Arsenal because I have the trust in this familiar environment."
No Real rift
Reports in Madrid suggested that Ozil had been allowed to leave after his professionalism and lifestyle were questioned.
But the Germany international insists his performances for Madrid, scoring nine goals in 32 games last season, prove his professionalism and commitment.
"I don't want to say anything bad about Madrid because I had three wonderful years there," he said. "I have great friends there and also we achieved a lot with the club.
"The people who know me, know how professional I am and I think over the past years one can see how many games I have played - 159 games - and if you are not professional in your life then I don't think you can play that many games.
"So people know how professional I am. This is what counts and I don't care about all the rumours.
"I have a new task here and I am just looking ahead. We have big goals and we will work very hard to achieve these goals."
With Czech midfielder Tomas Rosicky suffering a thigh injury on international duty, Ozil could be thrust straight into the starting XI at Sunderland on Saturday.
The German maintains he is ready for the hustle and bustle of the English top flight.
"Of course it is very physical here, but it is a man's sport and I am really glad to play in the best league in the world," Ozil said.
"I want to prove myself in England, therefore I look forward to playing here.
"I also played in the Bundesliga and Spain and always proved myself. I know that I will prove myself here as well."
You can see Ozil's first appearance in an Arsenal shirt on SNF. Game of the Day is from 8pm and Sunderland against Arsenal will feature in Match Choice from 10pm.