The 24-year-old sealed the €50 million transfer on Monday afternoon having undergone a medical in Munich, where he is on international duty.
Speaking to the club's official website, Wenger 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.
"I have said throughout the summer that we have been working hard to bring in top quality players to this football club. This has involved many, many people across the club and I have always had the full support of the club in making decisions on the football side.
"Mesut is a top quality footballer who will be a fantastic addition to our talented squad. We are all looking forward to him joining up with us after his international matches with Germany and working with us as an Arsenal player."
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