"I'm making this video for you as a message of gratitude for all the time we've spent together," Gomes began. "The last few weeks have been difficult, both for me and my family.
"My time in the blue shirt has come to an end, but I have to tell you how proud I am of all these years.
"This club is full of history, with great moments, but also with difficult situations that should make us learn from them.
"But both situations have one thing in common, your passion for this marvellous football club. The love. The tireless fighting spirit. Hard work. For me, there's another word that defines how special you are. Family."
Gomes continued: "Through ups and downs, incredible emotions and atmospheres, you never give up on us. You never give up on the person next to you. And that's what Everton is in the community.
"There are no words to describe the impact you have in helping others. I'm very lucky and grateful for all the experiences and moments we've shared together," added the Portuguese international midfielder, who made 14 official appearances for Everton last season, scoring two goals.
"I've met so many wonderful people and I'm touched by all of you who have made me and my family feel special. This message wasn't meant to be very long... but just a message of thanks wouldn't be enough," Gomes added.
"My family grew up under your protection and today I have my son singing Everton songs every day. I think you've done a great job, because I'm sure we'll never forget the time we spent with you. I'm not the best person to show emotions, but anyone who really knows me understands how much this means to me.
"People say that good things come to an end, and maybe that's the case, but I leave with my heart full of memories and wonderful moments... and for that I want to thank you.
"A final word to all the staff, players and officials I've had the chance to work with. You know how much I love you and how much I will miss you. Thank you so much. I want to wish you all the best for the future, because you Evertonians deserve it. Thank you, family. Always in my heart," concluded the 30-year-old midfielder, who is now a free agent.
The future of Gomes, who as well as Everton has represented Benfica, Valencia, Barcelona and Lille, could now lie in MLS, the top flight of the United States.