Gomes is expected to undergo his medical and complete his signing in Spain before traveling to Merseyside to be unveiled at Goodison Park.
Barca is to allow the Portugal international midfielder to spend the 2018-19 campaign in England on loan as he is not part of their plans.
The 25-year-old began his career at Benfica, with his career highlight being a European Championship win with Portugal in 2016.
His arrival at Everton will help to bolster the midfield options available to new Toffees boss Marco Silva.
Despite signing for a fee of €35 million (£31m/$41m) plus €20m in add-ons in 2016, he played only 46 times in La Liga since joining from Valencia.
Gomes will become Everton’s fourth signing of the summer transfer window