The 25-year-old attacking midfielder left Barcelona for the Emirates on Thursday in a deal reportedly close to £30m.
Sanchez netted twice during the World Cup finals in Brazil and he believes he can combine with Ozil to help the club win trophies.
Germany's Ozil joined Arsenal for £42m from Real Madrid last September and is currently preparing for this weekend's World Cup final against Argentina.
"With Ozil in the squad, Arsenal came close to winning the league title," said Sanchez. "I hope I can make a contribution so we can win as many titles as possible.
"The team not only plays really good football but the squad is really good and we can win silverware. We have a great squad, we are a big club and we can achieve big things.
"Playing regularly wasn't the only reason why I came here. I have come here to win the Premier League title, the Champions League and every title at stake. I am here to win titles and to achieve as much as possible."
Sanchez also paid tribute to manager Arsene Wenger, saying: "I know this club has a manager that looks after his players and takes care of them as well.
"I was told that he is a manager you can learn a lot with. He wants to achieve great things in football and that helped me make the decision to sign for Arsenal.
"Arsene Wenger's style of play is the sort of style the Chilean national team has, so therefore I am used to it. Arsenal plays very well, which fits my style. That is why I moved here.
"The manager has mentioned some certain positions but I am not worried about it right now. The manager and I will talk about my role as soon as I start training. Arsenal is a club that cares about its players and I can learn a lot here."
His first major game for his new club is likely to be the FA Community Shield against Manchester City on August 10.