The La Liga champions confirmed Mina's move for a fee of around £27 million, saying they had an option to buy him back.
Colombian centre-back Mina will join in a deal worth €30.25 million with another €1.5 in potential add-ons, Barcelona said.
Barca have inserted a buy-back option for the Colombian global, who caught the eye after a series of impressive performances at the Russia World Cup.
'I know about Everton's players and I look forward to being able to play with my new team. When I found out about this opportunity and what the manager wanted out of me I was happy.
Everton's season-long loan deal for Portugal's Gomes will see them pay 2.25 million euros and the player's wages.
"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".
Gomes joined Barca from Valencia in 2016, costing the club a reported €35million, but he has struggled to hold down a first-team place.
Mina, 23, only joined Barca six months ago from Palmeiras, but coach Ernesto Valverde has not been convinced by him and the club have chose to take advantage of his increased value following an impressive World Cup.
He joins former Barcelona team-mate Lucas Digne on Merseyside, and Mina added: 'The World Cup was incredible and I will never forget it, ' added Mina, who joins Lucas Digne in swapping Barcelona for Everton this month.