The 30-year-old midfilelder signs a four-year contract until 2022.
Nainggolan, who retired from the national team after being omitted from Roberto Martinez's World Cup squad, scored 28 goals in 155 league appearances for Roma and was instrumental in their run to the Champions League semi-finals last season.
"The conditions have been met for a deal for Radja Nainggolan," Inter's Sporting Director Piero Ausilio told the club's website earlier.
2018 Nainggolan Belgium
Image credit: Getty Images
"He is a top player. Everything will be made official tomorrow (Tuesday)and then we will say something more."
The 30-year-old 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.