The Belgium international re-joined the Blues in a £97.5m deal in the middle of August and has already found the back of the net for Thomas Tuchel's side, scoring on his debut against Arsenal.
The 28-year-old had seemingly settled at Inter following a difficult spell at Manchester United, but Lukaku has conceded that the lure of Chelsea proved to be too strong.
"I was only going to leave Inter Milan for Chelsea," Lukaku told HLN. "Kids love Real Madrid, Barcelona, Manchester United. And Chelsea for me, everyone knows what Chelsea means to me.
"If they ask me, why would I say no? I only realised that Chelsea was serious at the third offer. So it was €100m (£85m), then it was €105m (£90m), and then it went to €110m (£94m). Then I knew, this is truly serious.
"I was in a deep hole at Man United. I didn't want to go behind Inter's back. So after training I went to [Inter boss Simone] Inzaghi's office. I didn't want to ruin the atmosphere because I was no longer with my head in Milan. So I asked him: please find an agreement."
Lukaku, who has penned a contract with the Champions League holders until June 2026, scored 64 goals and registered 16 assists in 95 appearances for Inter. body check tags ::