The 25-year-old helped the Premier League side win the FA Cup last season, one of just 29 appearances in all competitions in 2014-15.
The Pole's departure follows Arsenal's signing of Czech international Petr Cech from champions Chelsea, with Szczesny already losing out last season to Colombian David Ospina in the pecking order.
Roma said Szczesny, who has made 181 appearances for Arsenal since his senior debut in 2009 as a 19-year-old, had signed a one-year contract on Wednesday after successfully completing a medical in Rome.
"I've come here to win games and trophies with AS Roma and I believe that the team is strong enough to do so," the Pole, who joined Arsenal's academy from Legia Warsaw in 2006, told Roma TV.
"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."
Arsenal said the loan move was subject to the completion of regulatory processes.
(Reporting by Alan Baldwin in London, editing by Pritha Sarkar)
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