The 29-year-old Belgian striker rejoined Chelsea for a reported £97.5m last August but admitted regretting the move in December and had a poor campaign.
The loan deal includes a £6.9m fee plus a potential £3.5m bonus, in which Inter will pay him in full with no obligation to buy.
Lukaku arrived in Milan on Wednesday, posing with an Inter scarf before completing his medical procedures and closing the deal.
“It’s a great feeling,” Lukaku told Inter TV. “What we achieved here a year ago was amazing. That benefits the team, the fans and me personally.
“Inter has given me a lot and I hope to do even better than last time. Now is the time to work hard as a team and hopefully do even better than before. “
Lukaku scored 15 goals in 44 appearances last season for Chelsea, scoring 30 as Inter win 2020-21 Series A Title.
“It’s like coming home. Me and my family have been very happy to be here thanks to my people, the fans and my teammates,” he said.
“From the first day I came here, everyone helped me settle down, I am very happy. I kept my home here when I came to the UK, so it makes sense.
“I’m delighted to be back and now I can’t wait to play with my teammates.”
The Belgian spent time with Inter president Steven Zhang, who has worked hard to bring the deal to fruition, while he revealed his immediate ambitions for the team.
“I think about the team more than myself,” he said. “I want Inter to win and I will do my best in training and playing to achieve that.”