The Belgium international impressed several clubs in the last campaign while playing for West Bromwich Albion, as he scored 17 goals for the Baggies.
Lukaku has admitted that he was pleased to have received recognition for his exploits but wants to find his feet at Jose Mourinho's side.
He told The Mirror: "It feels good. I knew that, if I performed well, people would make a lot of requests for me. But I'm a Chelsea player and happy to be here.
"It's up to me. If I do well, I will play. I have always felt like a Chelsea player, even at West Brom."
Chelsea recorded a 2-0 victory over AC Milan in their friendly clash on Sunday.