Ozil has signed for a Gunners record £42.4 million fee and immediately becomes the club's highest paid player.
Gazidis said: "This is an exciting day for all of us. We have signed a world-class player who is one of Europe's brightest young talents.
"Mr Kroenke, our controlling owner, has always fully supported Arsene and the club in making significant investments to strengthen our squad and to bring in talented players, who fit our style and ambitions.
"Like all of us, Mr Kroenke wants to see Arsenal winning titles and trophies and he has absolute faith and belief in our manager to achieve that. We will continue to work towards that goal and look forward to an exciting season."
For the big stories and the banter follow us on Twitter: @tribalfootball