The Belgium striker only scored eight goals in 26 Premier League appearances after his club-record £97.5million move back to Stamford Bridge last August.
Lukaku's second spell at Chelsea took another turn for the worse when he said stated in an interview with Sky Italia late last year that he was not happy with his role at the London club.
The 29 year-old declared: "I know I will return to Inter, I really hope so. I am in love with Italy."
He has now got his wish, sealing a switch back to San Siro for the 2022-2023 season less than a year after leaving for a huge fee.
"We're back baby. I'm very happy, thanks for the compliments. Remember three years ago, we were here? We're back," he said in a social media video alongside Inter chairman Steven Zhang.
Asked by Zhang whether he promises to 'score lots of goals at San Siro', he added: "That's what we're here for. I keep my promises."
Lukaku will try and help Inter wrestle back the Serie A title from city rivals Milan after he played a huge part in their Scudetto triumph in the 2020-21 season, scoring 24 goals in 32 league games.
During his previous two-year spell, no Nerazzurri player scored more goals (64), provided more assists (17) or created as many chances (133) in all competitions.
The former Manchester United and Everton frontman formed a fearsome partnership with Lautaro Martinez under Antonio Conte as Inter lifted their first league title in 11 years.
Lukaku is likely to also be joined by forward Paulo Dybala, who will reportedly join Simone Inzaghi's side after leaving Juventus as a free agent.