It has been over eight years since the Gunners last won a trophy, but the Russian billionaire, who owns just under 30% of the club, believes that the German's £42.5m arrival from Real Madrid was the dawning of a new era.
"In the past I tell the club that if they want to pretend to be number one in every tournament then they must have best players in the world, and if we don't have them in our squad we need to buy these in the market," he told BBC Sport.
"[Arsene] Wenger confirmed this by buying, for example, Ozil. Anything that gives to Arsenal, good results, is for us very good news. This is our mission and hope.
"I think we begin a new era for Arsenal where we win trophies. It's most important for football, winning trophies. We will be number one."
Ozil has scored two and assisted four in his nine Premier League appearances.