Lukaku scored eight goals in 26 Premier League appearances for Chelsea last season
The Blues signed the 29-year-old from Inter for £97.5m in August 2021, but he will return to the Serie A side having struggled last season.
The loan fee for Lukaku is about 8m euros (£6.9m).
The Belgium international scored 15 goals in all competitions for Chelsea last season, with eight in 26 Premier League appearances.
It is understood Lukaku was willing to take a pay cut to rejoin Inter, who won the Serie A title in 2020-21 with him leading their attack.
The Italian club's financial situation meant it was impossible for them to match Lukaku's wages or buy the frontman outright.
However, president Steven Zhang got involved personally in the negotiations on Monday, which was viewed as significant.
Lukaku, who left Chelsea to join Everton for £28m in 2014, returned to the Stamford Bridge side last summer on a five-year deal for a club-record fee.
However, he apologised for an interview during the season where he said he was not happy with his role under Blues manager Thomas Tuchel and wanted to return to the Italian club in the near future.
Lukaku scored only three times in his final 15 top-flight outings of the season as Chelsea's season fizzled out.
Tuchel's side finished third in the Premier League, while they were beaten by Liverpool on penalties in both the FA Cup and League Cup finals.
Inter finished second in Serie A last season, two points behind city rivals AC Milan. They are also in talks with Juventus forward Paulo Dybala.
The Argentina international, 28, is set to be a free agent when his contract expires at the end of the month.
-- Courtesy of BBC Sport