Colombia defender Mina, who impressed in the World Cup, could eventually cost €31.75million, while Gomes arrives on a season-long loan.
Mina had always been linked with a move away from Barcelona this summer with the club's purchases of non-EU players in Malcom, Arthur and Arturo Vidal filling their quote per La Liga's rules.
Silva has been desperate to bolster Everton's defence all summer and had been linked with a number of targets, such as Manchester United's Marcus Rojo and Newcastle's Jamaal Lascelles, but Mina was his top target.
Several Premier League sides including West Ham and Chelsea had been in the hunt for the Brazilian winger while AC Milan also expressed an interest.
The Toffees were not finished there as Barcelona confirmed the Toffees had signed both Mina and Gomes.
"Every discussion we've had was very important in making me feel his confidence about my game". This is a great opportunity for me and I am looking forward to competing here.
Gomes, who won the European Championships with Portugal in 2016, has found regular first-team football hard to come by at the Nou Camp since joining the Catalans in a big-money move from Valencia in 2016.
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