The Belgium international formerly represented the Premier League club between 2011 and 2014, spending most of that period out on loan.
Announcing the club-record €115m (£97.5m) transfer, Chelsea confirmed the 28-year-old has signed a deal through to 2026.
“I’m happy and blessed to be back at this wonderful club,’ Lukaku told the club site upon signing. “It’s been a long journey for me: I came here as a kid who had a lot to learn, now I’m coming back with a lot of experience and more mature.
“The relationship I have with this club means so much to me, as you know. I have supported Chelsea as a kid and now to be back and try to help them win more titles is an amazing feeling.
“The way the club is going fits my ambitions perfectly at 28 and just coming off winning Serie A. I think this opportunity comes at the right time and hopefully we can have a lot of success together.”
Chelsea director Marina Granovskaia added: ‘Romelu Lukaku is quite simply one of the world’s best strikers and goalscorers. We are absolutely delighted to be bringing him back to the club he loves, and are excited to be adding his talent to our Champions League-winning squad.”
Following loan spells at West Brom and Everton, Lukaku joined the latter on a permanent deal, before transferring to Manchester United in 2017.
He would leave United after two seasons, moving to Inter Milan in August 2019.
In his first campaign with the Italian side, Lukaku scored 34 goals in all competitions to match a club record set by Ronaldo in 1997-98.
Last season, the 28-year-old netted 24 times and recorded 10 assists in Serie A as he helped Inter to their first league title since 2010 – the club’s first trophy in a decade.
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