The 20-year-old joins for an initial fee of €13.4 million, the club said.
Depending on the achievement of certain performance targets, on the part of both the player and the club, the Giallorossi could pay up to an additional €1.5m in bonuses, read the club website.
The Turkey international has signed a five-year contract with Roma that runs until 30 June 2022.
“I'm delighted to be here and very excited about meeting the fans,” Cengiz was quoted as saying by the club website.
He said: “My aim is to earn myself a regular starting berth as quickly as possible."
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