The Chile star, who impressed at the World Cup, is confident the club are capable of adding further silverware next season after ending their nine-year trophy drought with the FA Cup win in May.
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"With [Mesut] Ozil in the squad Arsenal were [close] to winning the league title. I hope I can make a contribution so we can win as many titles as possible," he told the club's official website.
"We have a great squad and we are a big club. We can achieve big things.
"Playing regularly wasn't the only reason why I came here. I came here to win the league title, the Champions League and every title at stake."
Alexis also revealed Arsene Wenger's coaching pedigree was one of the main factors behind his move to Arsenal, with his admiration for his new manager a key pull in persuading him to join Arsenal.
"Arsene Wenger's style of play is the sort of style the Chilean national team has. Therefore I am used to it," he said. "Arsenal plays very well, which fits my style. That's why I moved here.
"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.
"I am certainly glad to be the first Chilean ever playing for Arsenal. I will do my best to achieve every possible thing with the club."