Mina, who was linked with a move to Manchester United, joins the Toffees on a permanent deal worth €30.25 million.
Gomes, meanwhile, will join the Toffees on a season-long loan.
Barca's statement on Mina and Gomes read:
FC Barcelona and Everton FC have reached an agreement over the transfer of the player Yerry Mina. The English club will pay FC Barcelona 30.25 million euros plus 1.5 million euros in variables. The Club reserves the right to buy back the player.
FC Barcelona would like to publicly express their thanks to Yerry Mina for his commitment and dedication and wishes him all the best for the future.
Shortly after the transfer of Mina to Everton, the loan deal of André Gomes also to Everton was made public. The two player will team up again with another ex-blaugrana, Lucas Digne, who made the move to the English club at the beginning of August.