Lukaku, 24, is on the verge of joining Manchester United after the two clubs came to an agreement over a £75million fee.
The Belgium international looked destined to seal a return to Chelsea, but the Red Devils beat them to it.
Lukaku, who has already completed his medical ahead of his switch to Old Trafford, is currently in Los Angeles with close friend Paul Pogba.
He is expected to join up with the rest of his new team-mates today for pre-season training.
No official announcement from Manchester United has been made yet, but Lukaku has thanked Everton for the four years he spent at Goodison Park.
He said on Instagram: “I want to say a big thank you to all the people involved at Everton.
“I want to thank the fans for your support throughout the four years we’ve spent together.
“You guys helped me through all my games and I can proudly say it was an honour to play in front of you.
“To the staff at the the stadium and training ground, thank you for making me feel at home from the first day I walked in.
“To my team-mates it was great to play with you guys. To technical staff thank you for helping me become a better player.
“Working with you guys has been a pleasure and I’ll take your advice throughout the rest of my career. Thank you Everton Football Club.”
The post was accompanied by a string of pictures of Lukaku wearing Everton‘s jersey.
And included popular chant ‘Forever Everton’.
Lukaku scored 87 goals in 166 games for the Merseyside club.