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Veretout made 131 appearances for the club in three seasons in the Italian capital, scoring 22 goals.
He also became a full France international, while he played his part as the Giallorossi won the Europa Conference League in May.
Here's what the Frenchman wrote:
"Morning Roma fans.
The time has come to say goodbye. After three amazing seasons, a new challenge awaits. I will never forget the years we have spent together. By some distance they have been the most intense of my career.
"In Rome I won a European trophy and I became a France international. And all of that is thanks in large part to you all. I want to thank the Roma fans for the incredible support. Rome is a city that gives you chills, the best in football.
"Together we have shared lots of victories and defeats, but you can rest assured that I never cheated you. I always gave my best. You all helped me to achieve my goals.
"Thanks to the club and the directors for their faith in me, thank you to my various coaches, my teammates, my 'warriors' and my brothers.
"I will never forget you!"
Imperium Partners
Centurion Partners
