The Poland international completed his move to the Serie A outfit on Thursday, having fallen down the pecking order at the Emirates Stadium.
Szczesny lost his place in the team after he was caught smoking following the club's 2-0 defeat to Southampton on New Year's Day, with David Ospina subsequently taking the No.1 spot.
The £11 million signing of Petr Cech from Chelsea this summer has further heightened competition in north London, and Szczesny says he did not hesitate to join the Italian club when he learned of their interest.
"It was an easy decision to join Roma; it is one of the biggest clubs in Europe," he said.
"For me to have an opportunity to come here for at least a year and show my qualities in a difficult league and the Champions League also, it is a fantastic experience. I think any player would be very proud to represent this club."
Szczesny will now face off with Morgan de Sanctis as he bids to become Roma's first-choice stopper, and he admits that he has been issued no guarantees about his selection by manager Rudi Garcia.
On his chances of being picked, he said: "I don't know. It's the manager's decision with how he is going to rotate the goalkeepers. I just hope I can earn my place in training.
"Playing games gives you a lot of experience and I believe I have plenty of it at such a young age. I hope I can use some of it to have a very good season here at Roma."
Arsene Wenger has insisted that the Pole's Gunners career is not over, but Szczesny maintains that he is unsure where his future lies.
"I don't know the outlook of the future. I'm very passionate about football and from what I've seen in the last few days in Italy, all the fans are very passionate so I'm sure I will have a good relationship with the fans," he added.
"I love to celebrate when we win and I get down when we lose. I love winning. That's what fans love the most, players who love to win."
