The Australia goalkeeper joins as a free agent after coming off contract at AZ Alkmaar this summer.
He arrives as cover for No1 Mile Svilar and said: "Mile looked great when he made his debut, then I remember his experience at Benfica. He arrived here last season and did very well, particularly in the second half of the season. I'm happy to come here and work with him and be able to push each other to do our best. I want to help Roma as a team and as a club, I can't wait to meet my teammates."
Ryan also spoke about coach Daniele De Rossi: “I remember the friendly against Roma in 2015 that I played with Valencia and he was there, I had recently signed for Valencia and it was the first time I played against a club with great tradition and in a match with two clubs with so much football history.
"When you play against people like Totti, Salah, De Rossi, you know it will always be a very demanding challenge. It was a great moment that marked the beginning of my career at Valencia. Certainly, De Rossi has done very well, since he took over he has achieved great results in Europe with a semi-final won. We can say that he is a coach who has a very important career ahead of him, I can't wait to be here and help the team and him, achieving the objectives."