The 24-year-old became the Gunners' club-record signing on Monday evening having undergone a medical in Munich, where he is currently on international duty.
Ozil's first-team options at Madrid were likely to become more limited after Real completed a world-record 100million euros deal for Gareth Bale and the former Werder Bremen midfielder admitted the chance to play for Wenger was a big factor in leading him towards choosing the Barclays Premier League club.
"I am thrilled to be joining a club of the stature of Arsenal and am looking forward to playing in the Premier League," he told Arsenal's official website.
"It will be great for my own personal development as a player and I am particularly looking forward to working with Arsene Wenger.
"From our negotiations it is clear the club has huge ambition and I look forward to being part of an exciting future."
Before Sunday's 1-0 win over big-spending Tottenham, Gunners boss Arsene Wenger had seen moves for Gonzalo Higuain, Luis Suarez and Yohan Cabaye all fail to materialise, but was finally able to land a big-name signing following the free transfers of Yaya Sanogo and Mathieu Flamini and a loan move for Palermo goalkeeper Emiliano Viviano.
The Arsenal manager was delighted to have landed a player of such a high calibre as Ozil.
He said: "We are extremely pleased to have signed Mesut Ozil.
"He is a great player, with proven quality at both club and international level. We have watched and admired him for some time as he has all the attributes I look for in an Arsenal player.
Source: PA
Source: PA