The 22-year-old Turkey international has been tipped for a bright future after impressing in his two-year stay at the club so far.
Under joined Roma from Turkish outfit Istanbul Basaksehir in the summer of 2017 and went on to score seven goals in 26 Italian Serie A appearances in his first season at the club.
Although his goal tally dropped to three with the same number of league games last term, Under made his mark in the UEFA Champions League, scoring three times in six games as Roma exited the competition at the round of 16 stage at the hands of FC Porto.
Under follows in the footsteps of fellow youngster Nicolo Zaniolo, who also put pen-to-paper on a new five-year deal recently.
“I arrived in Rome two years ago and since then, day after day, I’ve felt more in love with this city, this club and these fans,” Cengiz said.
“This is a very happy moment for me. I want to thank the club for allowing me to realise my wish to continue playing for Roma.”
Roma Sporting director Gianluca Petrachi added: “We really wanted to complete this renewal, because we all see the talent Cengiz has.”
“We are certain that over the coming years he will make a huge contribution to the quality of the team, realising his great potential here in Rome – the perfect place for him to continue to improve.”
Roma, who will be operating under a new manager in the shape of Paulo Fonseca, will begin their Serie A campaign against Genoa next weekend.