The 28-year-old Belgian landed at Biggin Hill airport on Wednesday evening, August 11, ahead of his move back to Stamford Bridge, after leaving the club back in 2014.
Lukaku passed the main part of his medical in Milan on Monday before flying to Nice for meetings with his agent Federico Pastorello in Monaco on Tuesday.
As reported by Sky Sports, the paperwork is now with club lawyers and once everything is agreed, Lukaku is expected to sign a five-year contract worth £200,000 a week.
After moving to Everton on a permanent deal, he later joined Manchester United and then Inter Milan in 2019.
Lukaku scored 64 goals in 95 appearances for the Serie A side and led them to the league title last season.