The Portugal international returns to Goodison Park on a permanent basis following a successful loan spell last season.
"Last year was a really good experience for me," Gomes said.
"I just wanted to feel part of something special and I found it here. It was good for me in that moment and right now, after signing for Everton, it's even better.
"I think the ambition from the club is not only for me, I think it's for all the players and the fans. We are all excited about that.
"I hope in the seasons to come we can enjoy more good football and win trophies. That's what we all want."
Sky Sports says the deal is worth £22m.