Lukaku, 29, endured a tough 2021-22 season following his €115 million move to Stamford Bridge from Inter last summer, scoring eight goals in 26 Premier League appearances.
His time at Chelsea was further hampered by controversy following an interview with Sky Sports Italia in which he stated he was "not happy" with the system that manager Thomas Tuchel was using.
The Belgium international returns to Inter, whom he helped secure the Serie A title in 2021 by scoring 24 times and assisting a further 10 in 36 matches in their league campaign.
"It's an amazing feeling," Lukaku told Inter TV. "What we achieved here a year ago was fantastic. That goes for the team, the fans and also me personally. Inter have given me so much and I hope to do even better than last time. It's now time to work hard as a squad and hopefully do even better than before."
He added: "It's like coming home. My family and I were so happy here thanks to the people, the fans and my teammates. From the first day I arrived here, everyone helped me settle in. I'm very happy. I kept my home here when I went to England, so that means something. I'm pleased to be back and now I can't wait to get out there with my teammates."
Sources told ESPN that Chelsea had originally demanded a loan fee of around €20m for Lukaku but eventually accepted a structured deal totalling around €12m including bonuses.
Sources also added that Inter will also cover the striker's £300,000-a-week wage.
Lukaku struggled to break into the first team during his first stint with Chelsea which ended in 2014.
ESPN's James Olley also contributed to this report.