The Turkey star has joined Leicester one a season-long loan deal with an option to buy.
Initially, an obligation to buy was being discussed, but it is now a €23m option.
— Leicester City (@LCFC) September 20, 2020
The 23-year-old has made 88 appearances for Roma with a return of 17 goals and 12 assists.
He links up with another Turkish international Caglar Soyuncu at the King Power Stadium.
In his first interview, Under said a move to England has been a long-time ambition.
“I can’t wait to go to Leicester and start training,” he said. “I’ve always wanted to play in England and this is a great opportunity to play in the Premier League.
“I’ll try to help my team-mates on the pitch and off the pitch and I believe that I can improve my performance every day.
“I think I am fast and can create lots of chances for my colleagues.
“I feel very good because my best friend plays for Leicester City. I’m very happy to be able to play with Caglar and I always watched Leicester’s games because of him.”