Lukaku is back at the club he initially signed for in 2011 and his club record move ends Chelsea's search for a central striker after their push to sign Borussia Dortmund's Erling Haaland came to nothing.
After winning the UEFA Super Cup following a penalty shoot out win against Villarreal on Thursday night, Chelsea have now added a key piece to their jigsaw with the addition of the 28-year-old Belgian forward.
"I’m happy and blessed to be back at this wonderful club. 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 said: "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.
"We are of course looking to build on last season’s success, and Lukaku will play a big role in achieving our targets. I’m sure all Chelsea fans will join me in saying welcome home, Romelu!"
Lukaku was at Chelsea for three years from 2011, the last two of which featured season-long loan stints with West Brom and then Everton.
He subsequently joined the Toffees in a permanent deal in the summer of 2014 and then moved on to Manchester United in 2017.
Lukaku scored 42 goals in 96 appearances for United across two seasons before then signing for Inter, for whom he has netted 47 times in 72 Serie A games, helping them win the title last term.
Lukaku is Belgium’s record scorer, with 64 goals in 98 appearances and his transfer is the most expensive sale ever sanctioned by an Italian club.
The Premier League website has updated Chelsea's squad list and suggested their new star striker will wear the No.18 shirt this season, but that has not been confirmed by the club.
Read an exclusive interview with Chelsea legend Joe Cole on Lukaku's return and the start of the Premier League season in this weekend's Sunday World