The Brazilian full-back, who joined the club from Torino in the summer of 2016, made a total of 132 appearances for the club in all competitions - scoring six goals.
With his contract expiring at the end of June, Peres has now agreed a move to Turkey.
"Thank you ROMA for these 5 years filled with emotions and great moments," Peres wrote on Instagram.
"I'm happy to have played for this club and it was an honour to represent these colours.
"I will never forget everything we've been through together, and I want to thank the fans and everyone who has supported me during my time here, and even those who have criticised me, for you made me grow stronger too - I will keep you all with me forever!"
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