The fee for the Germany international was understood to be £43million, making him the second most expensive player in Premier League history at the time behind Fernando Torres.
Ozil, who was 24, said in quotes on Arsenal'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 (then Arsenal boss) Arsene Wenger.
"From our negotiations, it is clear the club has huge ambition and I look forward to being part of an exciting future."
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."
Ozil went on to make just over 250 appearances for Arsenal in all competitions, scoring 44 goals, providing 71 assists and playing in three victorious FA Cup finals.
The playmaker left the club with a move to Fenerbahce in January this year, with his £350,000-a-week Arsenal contract having been due to expire in the summer.
He had not played for the Gunners since March 2020 and had been omitted from their Premier League and Europa League squads by boss Mikel Arteta, who said leaving him out had been "just a football decision".