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."
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. I have great friends there. We achieved a lot with the club and (won) trophies. That is why I don't want to talk a lot about it," Ozil told a press conference.
"People who know me know how professional I am and I think [in] the past years, you can see how many games I played - 159 games.
"If you are not professional in your life, then I don't think you can play that many games.
"People know how professional I am and this is what counts. All the rumours, I don't care about them.
"I have a new task here. I am just looking ahead.
"I am in London now. We have big goals here and we will work very hard to reach these goals."
Ozil added: "You can see by the reaction of the fans and the players that they didn't understand the move, but this is football. You always have to look ahead and I have made the next step.
"My time there (Real Madrid) was great, but that topic is over.
"I will have wonderful years here (at Arsenal), hopefully I will win many trophies and stay healthy and this what I look forward to."
Ozil, who was part of the Germany Under-21 side which beat England 4-0 in the final of the 2009 European Championships, is in no doubt he has signed for a club and manager capable of taking his game to another level.
"I am in the strongest league in the world and have to prove myself here to continue developing here. This is why I am at the right club," he said.
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."
Ozil insists he will not let the huge price tag play on his mind.
"I would have come here without a fee, that wouldn't have been a problem," he said.
"Of course I am proud of this (being Arsenal's record signing), but the most important thing for me is that the manager trusts me, that I can get trust from him.
"This was the crucial point for me and this is why I have come here."
Wenger is confident Ozil will fit right in with the dynamic of his side.
"He has a style of play which can integrate with our style because we have a game which is based on movement, technical ability and creativity - he has all the attributes to be one of the leaders of our team," the Arsenal boss said.
Jack, Ozil providing the sparks needed....flamini being the spine of defence in mid, I can't wait for may.....- eijnaix