The 23-year-old spent last season at Stoke and suffered relegation from the Premier League.
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.
"The manager made me feel confident about playing here".
Mina and Gomes are expected to undergo their medicals in Barcelona as there is little time for them to travel to England to complete the formalities of the transfer.
The Toffees were in desperate need of a new centre-back after a disastrous campaign that had its roots in the defensive frailties.
Late move: Barcelona defender Yerry Mina, who starred at the World Cup for Colombia, is off to Everton.
Upon joining Everton, Mina told evertontv, "It is important that the club want to fight for something".
The winger, 20, wanted to leave for Red Bull Leipzig following a loan spell there last term, but Everton blocked it. This is why I am here.
Everton and Fulham stole the show on the Premier League's transfer deadline day, as both clubs welcomed several eye-catching signings. Six months later and after a good World Cup, they have moved him on for nearly three times what they paid for him, despite him never quite performing during his short stay. This is a great opportunity for me and I am looking forward to competing here.