The 29-year-old Belgian forward had re-joined Chelsea for a reported 97.5 million pounds in August last year but admitted his regret about the move in December and had an underwhelming campaign.
The loan deal included a 6.9m pounds fee plus 3.5m pounds in potential bonuses, with Inter to pay his wages in full with no obligation to buy.
Lukaku arrived in Milan on Wednesday, posing for photos with an Inter scarf before completing his medical and finalizing the deal.
“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.”
Lukaku netted 15 goals in 44 appearances last season for Chelsea, having scored 30 times as Inter won the 2020-21 Serie A title.
“It’s like coming home. My family and I were so happy here thanks to the people, the fans and my team-mates,” he said.
“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 team-mates.”
The Belgian spent time with Inter president Steven Zhang, who worked hard to bring the deal to life, while he revealed his immediate ambitions for the side.
“I think about the team more than myself,” he said. “I want Inter to win and I’ll give everything in training and in games to achieve that.”