The Manchester United striker has a deal in principle to land £180,000-a-week wages when a fee is agreed between the clubs.
Lukaku will be allowed to leave for £75million after losing his place under Ole Gunnar Solskjaer.
And the 26-year-old is ready to move to Italy to get his career back on track under ex-Chelsea boss Antonio Conte.
He held showdown talks with United officials last month when he cut short his holidays to discuss his future.
United have agreed to let him go for the fee they paid Everton two years ago, allowing his agent Federico Pastorello to assess the summer market for his new client.
Pastorello publicly stated Lukaku would be assessing his future at United and Inter are the clear frontrunners despite interest from Juventus.
United are prepared to allow the Belgium international to leave despite his scoring rate of a goal every two games of action.
His move comes with the blessing of national team coach Roberto Martinez, who says the striker needs to find the right club.