The 29-year-old only returned to Stamford Bridge last summer on a five-year deal having helped Nerazzurri win the Serie A title in 2020/21.
The temporary move to Italy brings the curtain down on a frustrating first full season back with the west London club.
The Belgium striker said before Christmas he was "not happy" and hoped to re-join the Milan giants.
He later apologised for his comments but scored only three times in his final 15 Premier League games of last season.
Lukaku made only 16 starts in the Premier League - and a further 10 from the substitutes' bench - and scored eight goals in the top flight.
Despite an underwhelming campaign, he still finished the season as the Blues' top scorer with 15 goals in all competitions.
Lukaku first left Chelsea in 2014 to join Everton for £28million before joining Manchester United for £75million in 2017.
He then left Old Trafford in 2019 to sign for Inter for £73million on a five-year deal, having scored 42 goals in 96 appearances.
Lukaku scored 47 Serie A goals in 65 top-flight starts for the Milanese giants and helped the club win a first Scudetto in 11 years in his final season with them in 2021.