The Polish goalkeeper has slipped down the pecking order following the arrival of Petr Cech from Chelsea last month and Szczesny will now attempt to make his mark in Serie A.
Szczesny told the Roma website: “I’ve come here to win games and trophies with Roma and I believe that the team is strong enough to do so.
“I think there’s great potential. I know the faces of the players and I know their names, so hopefully I will settle in very quickly.”
Szczesny made his Arsenal debut in September 2009 and has made 180 appearances for the club in all competitions and Arsene Wenger insists he has a long-term future at the Emirates Stadium.
He played 33 games for them and Poland last season but only appeared in FA Cup matches after a 2-0 Premier League defeat at Southampton on January 1.
Szczesny was at fault for both goals at St Mary’s and was later fined and dropped for smoking in the dressing room, with David Ospina replacing him as No 1.