The 26-year-old Portugal international had surgery to repair a fracture dislocation suffered in Sunday's 1-1 draw with Tottenham.
Speaking for the first time since the injury he said: "As you already know everything went well.
"I am already at home with my family. I would like to thank you all for the supportive messages."
A club statement said the surgery on Monday "went extremely well" and on Wednesday, manager Marco Silva said the club had received "really good" feedback on Gomes, who has already visited team-mates.