The clubs are working on the final details of the deal, which will see Lukaku join the Blues on a five-year contract.
Inter have previously rejected two offers from Chelsea for the Belgium international, the second of which was worth £85m (€100m) plus left-back Marcos Alonso.
Romelu Lukaku earlier in the week instructed Inter Milan to allow him to leave if a suitable offer came in; the Belgium international scored 24 goals as the Nerazzurri won Serie A last season; Lukaku expected to sign a five-year deal with Chelsea
Lukaku, 28, left Chelsea in 2014 after making just 15 appearances there following his arrival at Stamford Bridge from Anderlecht in 2011.
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