"Inter were the only club I wanted," Lukaku told the clubs official website.
"I'm here to bring the Nerazzurri back to the top," he added.
For some of the transfer window, the 26-year-old had been linked with Serie A and fierce rivals - Juventus - who was in advanced talks with Lukaku as part of a swap deal.
Leaving Old Trafford
Lukaku left the club having scored 42 goals in 96 matches after signing from Everton back in 2017 for a fee of £75 million.
He struggled for form last season and drifted in and out of the team and scored just 15 goals in 45 appearances.
Whilst he struggled last season, he has been a success in the Premier League. A dangerous centre-forward who always keeps the defence on their toes.
His overall contribution to English football is impressive. Having scored 113 goals in 252 appearances.
A chance at redemption
Having said that last season Lukaku struggled with form, he was not shown much love by the supporters at Man Utd. He was often slated by pundits too.
While most players can take criticism, it was clear that it was affecting his performances. This is what makes his move to Italy interesting.
Demands are high, especially at clubs like Inter. With a manager like Antonio Conte, the demands multiply.
While he was out of form last season - this is a fresh start. This is a club who stopped at nothing to ensure they got their man.
With fans flocking to the airport in the early morning to greet him, he must feel like this is his chance to silence his critics. He has been shown a lot of love since arriving in Milan.
With a manager who was desperate to have him in the squad, fans singing his name, this is a huge move for Lukaku. One that should see him score goals and regain confidence while playing for one of the biggest clubs in the world.