The Blues will pay £28 million for the Belgium international, as the player verbally agrees to sign a five-year deal with the Premier League champions.
He will become Antonio Conte's first signing after the Italy boss agreed a deal to replace Guus Hiddink after Euro 2016.
Chelsea's deal for the box-to-box midfielder has been thrashed out over the last 48 hours with Roma and the player's representatives.
Roma's director of sport Walter Sabatini was spotted outside Stamford Bridge on 7 April and set up a meeting with Chelsea's transfer bosses, witht the Belgian midfielder Conte's number one target to strengthen his midfield.
Conte is an expert in the Serie A transfer market and knows that Roma often sell one of their best players every year to ensure they balance their books as they struggle to compete with Juventus on a financial and sporting level.
The 46-year-old has been linked with further business with Roma and former club Juve, and is thought to be targeting Kostas Manolas and Leonardo Bonucci in a bid to strengthen his defence.
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Roma director Sabatini was resigned to losing his star midfielder and admitted on Tuesday that "Nainggolan is a universal midfielder, so strong in every area of the game that he is wanted by many clubs".
Roma and Chelsea won't make the transfer official until after the current season but Roma's representatives told Goal: "I know there is a Chelsea interest in Nainggloan but he is our player and we are happy with him, we cannot speak about the transfer market at this time."
Nainggolan's style of play is thought to be well suited to Premier League football and his signing may cast doubts over Jon Obi Mikel's future at the club.