Mina's was impressive during this summer's World Cup and scored a last minute equaliser against England in their last-16 tie, one of three goals he netted in Russian Federation.
Barcelona said they reserve the right to buy Mina back, while Gomes has cost Everton a £2m loan fee.
There was a predictably frantic conclusion to the last hours of business, the Premier League waiting to register ten players after the 5pm deadline, deal sheets submitted pending medicals and the agreement of personal terms.
Linked to the likes of Chelsea throughout the summer, Brazilian Bernard admitted a conversation with Marco Silva persuaded him to move to Everton.
After penning his deal, Mina revealed a Premier League move was impossible to resist and wants to help Everton progress under new manager Marco Silva.
'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".
In March, having endured consistent criticism for failing to live up to his Valencia form, the 25-year-old described his Barca spell as "a kind of hell", admitting he had struggled with depression. "I am also determined to do my best for Everton".
"Every discussion we've had was very important in making me feel his confidence about my game".