The Belgium international has returned to Stamford Bridge following a successful loan spell at West Bromwich Albion, where he scored 17 league goals for the Baggies.
The 20-year-old had been linked with another temporary switch away from west London but newly-appointed Blues boss José Mourinho appears prepared to hand the forward a chance to impress at his parent club.
And the striker says he is determined to work hard in an attempt to become “twice as good” next season.
Lukaku wrote on Instagram: “I will train every single part of my body to be twice as good as last year.
“Stronger, faster, bring more quality into my game just to be as deadly as the great masters of the game.
“It will be hard but when you work hard you play hard. Season 13-14 is the season when I stop playing like a boy and will play as a MAN!! #ambition.”