The Germany playmaker completed a €47 million move from Real Madrid on deadline day, becoming Arsenal's fourth signing of the window following Yaya Sanogo, Mathieu Flamini and Emiliano Viviano.
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"It definitely shows a statement that we are ready to step up," Walcott told reporters.
"We had a disappointing start to the season, but we have bounced back and it is looking fantastic now.
"With the likes of Ozil joining the club, it is only going to boost everyone."
Ozil, who scored nine and assisted 16 goals last season, is in line to make his Arsenal debut when they travel to Sunderland on September 14.