The 20-year-old scored 17 Premier League goals while on loan at West Brom last term and previously said he would like to stay at The Hawthorns for another year.
But a conversation with Mourinho has convinced the Belgium striker he can compete for a place with the likes of Fernando Torres and Demba Ba and still fulfil his dream of going to next summer's World Cup finals.
"I always said my ambition was to play for Chelsea," said Lukaku, who cost £18m when he arrived from Anderlecht in August 2011.
"Now I will go back to Stamford Bridge and try and play even more games than I did at West Brom. If I can score a few early on, it can turn into a really good season for me.
"I have had a good conversation with Jose Mourinho, and I know it's up to me to show I'm worth a place.
"It is the World Cup next year, and I need to be playing. But if I don't get in the Chelsea team often enough, then I won't deserve to be in the national squad.
"I am not afraid of that. I am determined to succeed with Chelsea next season. I want to prove myself.
"People will compare me with Didier Drogba, and he was always my hero. But I am my own man, and I want to be known for what I do."