The Belgium international is set to move to Stamford Bridge from Inter , who have accepted an offer of £97.6m for their star striker.
According to The Athletic, Lukaku will undergo a medical in Belgium on Sunday before flying to London within 24 hours.
The striker will sign a five-year contract worth around £195,000 per week after tax, making him the highest earner at the club.
Talks between Chelsea and Inter accelerated on Friday as the Blues attempted to tie up the deal before the start of the Premier League season.
Chelsea had initially tried to lower the fee by offering fringe players in part-exchange, but Inter insisted on a cash-only deal to help ease their financial concerns.
Manchester United will receive around £3.4m due to a sell-on clause they inserted in the deal that took Lukaku to Inter in 2019.
The report adds that while the 28-year-old was happy in Milan, the chance to return to Chelsea proved too good to turn down.
The Blues are the only Premier League club Lukaku would have been willing to join this summer.
The Belgian departed Stamford Bridge in 2014 after just 15 goalless appearances for Chelsea, but he will now spearhead Thomas Tuchel’s attack.
He may prove to be the missing piece in the jigsaw. Kai Havertz performed well as a false nine under Tuchel last term, but it was clear that Chelsea needed to strengthen up top.
Tuchel has never really taken to Tammy Abraham, who could be on his way to Atalanta, while Olivier Giroud has joined AC Milan .
Lukaku left Chelsea as a work in progress, but he returns to the club as the finished article.
The Belgian scored 64 goals in 95 appearances for Inter, whom he fired to the Serie A title last season.
Lukaku will now be aiming to do similar for Chelsea in 2021/22.