The Belgium international returned to Stamford Bridge this summer after spending the 2022-23 campaign on loan at Inter Milan.
Inter were keen to bring Lukaku back to the club, but pulled out of a potential deal after learning he had been in discussions with rivals Juventus.
While a move to Juventus ultimately failed to materialise, Lukaku also turned down the chance to join Saudi Pro League side Al-Hilal.
Chelsea had been determined to sell Lukuku this summer, but they have been forced to consider loan proposals after finding it difficult to find Lukaku a new club.
Roma identified Lukaku as a potential target and duly sent club president Dan Friedkin and director Tiago Pinto to England to discuss a deal.
According to The Telegraph, Roma have now reached an agreement with Chelsea over a season-long loan deal.
Chelsea were keen to secure a £8m loan fee, but have compromised on just over £5m, so they do not have to contribute to the player's salary.
Lukaku, who has agreed to take a pay cut on his £320,000-per-week salary, will earn around £6.4m during his time in the Italian capital.
While Lukaku has agreed to take a further pay cut should he return to Chelsea next summer, the Blues have agreed to insert a £37m release clause into the player's contract.
Lukaku is scheduled to fly with Friedkin and Pinto to Rome on Tuesday, and he will undergo a medical before being unveiled as the club's latest summer addition.
The striker will reunite with his former manager Jose Mourinho after the pair worked together at Manchester United during the 2017-18 season.
Mourinho has been determined to strengthen his forward line this summer, with Tammy Abraham sidelined for an extended period due to an anterior cruciate ligament injury.
Lukaku is now set to become the second forward to join the Italian club in a matter of days after Sardar Azmoun recently completed a loan move from Bayer Leverkusen.