The 30-year-old was instrumental in Roma's run to the Champions League semi-finals last season.
Inter confirmed the move on Monday with sporting director Piero Ausilio saying, "The Belgian is a real coup for Inter. He is an important player and one that has always been decisive, particularly during his years with the Giallorossi..."
Roma said that the transfer agreement also includes a sell-on clause if Nainggolan leaves Inter in the future, with the Giallorossi entitled to 10 percent of the transfer fee -- up to a maximum of two million euros.
Nainggolan will be reunited with manager Luciano Spalletti as Inter look to push on from last season's fourth-placed finish which saw them qualify for the Champions League for the first time in six seasons.
Meanwhile, Italy defender Davide Santon has moved to Roma from Inter on a four-year contract for a fee of 9.5 million euros.
The 27-year-old, who has eight caps for Italy, made 110 appearances for Inter across two spells at the club.
"I cannot wait to get started and show everyone what I can do," Santon said on Roma's website http://www.asroma.com/en/news/2018/6/roma-complete-santon-signing.
"Coming to Roma means a lot to me, I really wanted to make the move and being here now has given me a lot of motivation."
Roma have also signed 18-year-old midfielder Nicolo Zaniolo from Inter on a five-year contract.
(Reporting by Arnab Paul and Aditi Prakash in Bengaluru; Editing by John O'Brien, William Maclean)
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