The Polish goalkeeper has lost his place in Arsene Wenger’s side after Petr Cech signed from Chelsea last month.
Sky sources reported last week that Arsenal and Roma were in talks over a deal and Szscesny took to social media to inform fans he is making the move, addressing viewers in a 10-second video.
Speaking in Italian, he said on Sunday: “Good evening Giallorossi. I am very happy because I am going to Roma tomorrow. I’ll see you soon.”
Szczesny then signed off with a wink and an announcement on his future is expected at some point on Monday.
The 25-year-old made his Arsenal debut in September 2009 and has made 180 appearances for the club in all competitions.
He played 33 games for them and Poland last season but only appeared in FA Cup matches after a 2-0 Premier League defeat to 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.