Gomes sealed a move to Goodison Park on transfer deadline day, and will now spend the 2018-19 campaign on loan at the Merseyside giants.
The 25-year-old, who has previously been linked with Manchester United, Tottenham Hotspur and West Ham United, also branded Everton a "fantastic club" upon his arrival.
"I'm delighted to sign for this fantastic club - it's a good day for me," Gomes told Everton's official website. "Everton always was a big option for me, especially after speaking with the coach, Marco Silva.
"Every discussion we've had was very important in making me feel his confidence about my game. Everybody in Portugal knows how Marco Silva works and his abilities as a coach.
"For me, it was really good to speak to him because I know how good he is and I feel motivated to work with him and to play for Everton, a great club."
Gomes made 31 appearances for Barcelona in all competitions during the 2017-18 campaign.