The veteran 'keeper joined the Gunners from rivals Chelsea earlier this week.
It has been hailed as a fantastic signing by manager Arsene Wenger, as he looks to build a side that is capable of challenging for major honours once again. Cech won everything with the Blues and says he believes he will win trophies at the Emirates.
"I believe I will win trophies at Arsenal. It is as simple as that," he told Arsenal.com.
"Winning the FA Cup is great for the club and great for the confidence of the players’ mentality. I believe there is a nice platform for Arsenal to build on and I hope in the new season we will make another step forward.”
Wenger has been active in the transfer market in recent seasons, with Mesut Ozil arriving in a big-money move from Real Madrid two summers ago, while Alexis Sanchez joined from Barcelona last term.
Several young players also impressed during the last campaign and Cech believes that balance of quality, talent and youth can see them lift more trophies in the future.
"There is a great balance between the experienced and the young so there is no reason why I wouldn't think that I am going to win trophies,” he added.
"In the Arsenal squad we have World Cup winners, a guy who has won the Champions League, so many internationals with vast experience and many talented players who will want to prove a point and win the league and the Champions League."
More additions needed
Given their performances during 2015 so far, there is certainly no reason not to believe Arsenal can challenge on all fronts next season.
The addition of Cech has pushed them further towards being a more capable side, with his experience and overall quality seriously improving arguably the weakest area of their team.
If they were able to add a top-quality defensive midfielder to their side this summer, as well as another centre-forward, there is no denying they would have a squad that would take some effort to beat.