Mina has signed on a permanent five-year deal worth €30million (approx £27.2million), while Portugal global Gomes has arrived at Goodison on a one-season loan.
The Brazil winger, a free agent having allowed his contract with Ukraine's champions to expire at the end of last season, signed a four-year contract at Goodison Park.
In the immortal words of one Larry David: preeeetty... preeeeetty... pretty good.
"I'm delighted to sign for this fantastic club - it's a good day for me", said Gomes to Everton's in-house TV channel.
Manchester United, meanwhile, have since had an approach for Atletico Madrid defender Diego Godin knocked back by the Spanish club.
Speaking about why he wanted to join, the 23-year-old told the club's website that he discussed Everton with fellow teammate Lucas Digne - who played alongside Mina at Camp Nou - before making the switch.
A loan fee of around £2million was agreed, with Everton also picking up the cost of the player's wages. 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.
Everton brought in three new faces on the final day of the Premier League transfer window, swooping for Brazilian midfielder Bernard from Shakhtar Donetsk and Barcelona players Yerry Mina and Andres Gomes.
Everton coach Marco Silva finally convinced Gomes to join and he has had his medical for the Premier League side in Barcelona.