Colombian centre-back Mina will join in a deal worth €30.25 million with another €1.5 in potential add-ons, Barcelona said.
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.
He has played 14 times for Brazil, scoring once, with his last global appearance coming at the 2014 World Cup.
"I know about Everton's players and I look forward to being able to play with my new team".
'They are historically among the four most successful clubs in England and when I found out about the club and what the manager wanted from me, I was happy.
Everton begin their Premier League campaign away to Wolves at Molineux on August 11 before they host Southampton on Merseyside a week later on August 18.
West Ham and Arsenal were touted with interest in Gomes up until he suffered an injury in pre-season for Barcelona. The club reserves the right to buy back the player.
The 25-year-old has played 29 times for his country.