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The 23-year-old has spent the last three years of his career at Stadio Olimpico, but will now link up with fellow countryman Caglar Soyuncuat the King Power Stadium.
The Turkey international is looking forward to working with Soyuncu at club level and also says he is relishing the chance to prove himself in the English top flight.
Under told Leicester's official website after his unveiling: “I can’t wait to go to Leicester and start training. I’ve always wanted to play in England and this is a great opportunity to play in the Premier League.
“I will 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 am very happy to be able to play with Caglar and I always watched Leicester’s games because of him.”
Roma invested €13 million (£12m/$15m)in Under's talents in the summer of 2017, snapping him up from Basaksehir on a five-year contract.
The Turkish winger has since racked up 88 appearances across all competitions for Paulo Fonseca's side, scoring 17 goals and providing 12 assists.
He was rewarded for his performances with a new long-term contract in August 2019, but only featured in 18 Serie A matches for Roma last season.
Under will now be expected to help Leicester build on a fifth-place Premier League finish, with Brendan Rodgersleading the club during their first foray into the Europa League.
The Roma star will not be eligible to feature when the Foxes take on Burnley at the King Power this weekend, but could be in line to make his debut during an EFL third-round clash against Arsenal on Wednesday.