The 20-year-old Turkey international moved to the Stadio Olimpico on an initial season-long loan earlier this month after spending two seasons with the Turkish champions.
Roma can extend the loan for another year, at no additional cost, and also sign the player permanently in the 2016-17 season for a fee of €11 million.
Ucan is keen to show his worth as Rudi Garcia's side seek to improve on finishing second last season.
"I put in some big performances at Fenerbahce. [Roma's director of football Walter] Sabatini wanted to sign me on the back of the success I had there," he said.
"There are lots of great midfielders at Roma who can lead the team to success. I have to get used to the way they play.
"I feel I'm a midfielder but I'm used to playing in different areas of the field so I can play in the hole, too.
"This is a new adventure for me and I'm going to work hard to help take Roma to the top."
Ucan initially joined Fenerbahce from Bucaspor in 2012 - going on to make 25 Super Lig appearances for the club.
He added his thanks at being offered the chance to join Roma.
"I'll always be grateful to Sabatini and Garcia, they worked really hard to bring me here," he added.
"My first few days with my team-mates have gone very well, even though I don't speak Italian yet."
