Under is manager Brendan Rodgers’ second summer signing after Atalanta’s Timothy Castagne arrived earlier in the transfer window.
Leicester have the option to make Under’s move permanent at the end of his loan spell for £22m.
The 23-year-old Turkey international joined Roma from Istanbul Basaksehir in the summer of 2017 but could not command a regular starting berth in his time at the club.
He however showed glimpses of his quality when given the chance and scored 17 goals in 88 appearances across all competitions in the Italian capital.
Under will link up with compatriot Caglar Soyuncu at his new club, and has expressed excitement with the move to the Foxes.
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.”
Under will be unavailable to face Burnley in the Premier League on Sunday but could make his debut against Arsenal in the League Cup on Wednesday.
