The 24-year-old has signed a five-year contract said to be in the region of £130,000 a week at the Emirates.
Ozil declared that the faith shown in him by Wenger made his mind up over a move to the Emirates, a challenge he is relishing.
He told the club's official website: "I am thrilled to be joining a club of the stature of Arsenal and am looking forward to playing in the Premier League.
"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."
Manchester United and Paris Saint-Germain were linked with moves to hijack Arsenal's bid but they didn't sway Ozil, who will wear the number 11 shirt at the Emirates.