The move marks a return to Italy for Lukaku, who spent two seasons at Inter Milan between 2019 and 2021 and returned on loan last season.
Chelsea were keen to offload Lukaku this summer amid an overhaul of the squad at Stamford Bridge. ESPN previously reported that Lukaku rejected a proposal to join Saudi Pro League club Al Hilal. A deal with Juventus also broke down, while Inter Milan had two bids rejected.
Sources have told ESPN that Roma will pay up to £8 million ($10.1m) in a loan fee depending on performances.
Chelsea were willing to sanction a loan deal to Roma, but were keen for his new club to take on the bulk of his wage, which is around £300,000-a-week.
Information from ESPN’s James Olley contributed to this report.