Lukaku is expected to join up with Manchester United on Monday after Jose Mourinho's squad flew out to the USA for their pre-season tour on Sunday.
The move will bring an end to Lukaku's four-year stay at Goodison Park - one of which was spent on loan from Chelsea - and the 24-year-old took to Instagram to thank the club's players, staff and fans for all the support they have given him.
Lukaku wrote: "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 stadium and training ground, thank you for making me feel 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."