The in-demand midfielder has joined on loan from Cagliari for €3 million with the option to spend €6m more at the season's end to buy half of his contract
Both clubs confirmed the initial €3 million deal - which was considered a certainty as the Giallorossi trumped interest from potential suitors such as Napoli - on Tuesday.
Should Roma choose to extend Nainngolan's stay beyond this campaign, it will cost them an extra €6m to buy half of the 25-year-old Belgium international's contract.
"For a Sardinian, it is difficult to leave the island," Nainggolan told Cagliari's official website. "It is for me, now that I have become Sardinian adoption.
"On the one hand I'm happy because the transfer may be an important step in my football career, on the other hand I am sorry because I am leaving the place where I grew up as a man and as a footballer.
"I was convinced that this club we could do something important, but unfortunately there were issues that stopped us from realising such a project.
"I hope that this situation can be resolved as soon as possible because the city of Cagliari deserves much more than they have received in the past three years.
"I will never stop thanking the chairman, my team-mates and the coaches that I have had during these seasons here. Thanks to them I have become what I am today.
"Not least thanks to the fans who have always supported me and made me become the biggest fan of this team.
"For Cagliari, I always gave my best. Today ends one journey, but another begins, but these years I always keep those memories inside."