Arsenal's chase for the German playmaker dominated Monday's transfer deadline day, with the Gunners finally getting their man before the 11pm closure of the window for a club-record fee believed to be £43million.
Ozil admitted on Tuesday that Gareth Bale's arrival at the Bernabeu convinced him the time was right to leave Real Madrid - and the 24-year-old is now keen to prove that he joined "the right club".
In an exclusive interview with Sky Deutschland, Ozil said: "I feel confident that our team will reach our goals. We have a very young and capable squad full of players who will grow stronger.
"I feel positive and I say: 'Let's go Gunners'.
"The Premier League is the strongest league in the world and it's a challenge for me as I want to prove myself and prove I'm with the right club - one that supports me and supports the important players in my side.
"I just can't wait and I'm looking forward to it as the fans are very emotional in England - they're crazy about football and I'm looking forward to taking on the league."
Ozil believes he can thrive in England's top tier under Arsene Wenger, having held lengthy conversations with the Arsenal boss on the telephone.
In an interview with the German Football Association's official website, Ozil said: "At the weekend, I was certain that I would stay at Real Madrid.
"But afterwards I realised that I did not have the faith from the coach or the bosses. I am a player who needs this faith and that is what I have felt from Arsenal, which is why I have joined.
"I am a player who needs this faith and that is what I have felt from Arsenal, which is why I have joined.
"I am really looking forward to it because I have the faith of the coach. I had spoken to him at length on the telephone, he explained his plans and that he has faith in me - that is what I need as a player."