The centre-back, who was in the sights of Manchester United until they withdrew their interest and was close to joining Lyon, has signed a five-year deal, while Andre Gomes followed the same path on loan.
Although Barca have included a buy-back option in the agreement, the Colombia defender departs Camp Nou just seven months after arriving from Palmeiras, having failed to dislodge Samuel Umtiti or Gerard Pique in his bid for regular minutes.
And Mina is determined to show his quality in the Premier League, adding that the chance to play alongside Gomes and Lucas Digne - who made the same switch last week - played a part in his decision to join the Goodison Park side.
"It is important that the club want to fight for something. This is why I am here," he told his club website.
"I have watched the Premier League for a long time. It is the best league in the world. This is a great opportunity for me and I am looking forward to competing here.
"I know about Everton’s players and I look forward to being able to play with my new team. I have spoken a lot to the coach and I know his passion for Everton and determination to be successful. I am also determined to do my best for Everton.
"I spoke to Lucas and he told me all about the club, which also made me keen to come here.
"I spoke with Andre, too. He is a good guy and we want to do our best for Everton."
Coach Marco Silva was delighted to welcome the defender to the club and hopes to capitalise on his aerial ability.
“Mina is a quality player, a good defender, strong in the challenge and in the duels," he said.
"He has good knowledge of the position he plays and he is good on the ball as well. He will contribute in the build-up play and will also be very strong at defensive and offensive set-pieces."