The fee for Mina, who only joined the Spanish champions in January, could rise by €1.5 million and Barcelona have inserted a buy-back clause in the player's contract.
Barca can re-sign the defender for a cool €60m.
It was also a good day for Leicester City, who, not only managed to keep hold of Harry Maguire amid reported interest from United, but also brought in the well-regarded young defender Caglar Soyuncu from Freiburg, tied Jamie Vardy down to a new deal and signed Croatia Under-21 global Filip Benkovic.
Having already taken Lucas Digne, Everton signed Yerry Mina and Andre Gomes on Thursday after some complicated negotiations, with the deals being confirmed around the closure of the window in England.
Bernard, 25, left Shakhtar Donetsk when his contract expired and had been linked to a host of European clubs. When I found out about this opportunity and what the manager wanted out of me I was happy. I know about Everton's players and I look forward to being able to play with my new team.
Moments later they also confirmed that Portugal worldwide Gomes would join the Premier League side on loan.
Andre Gomes, meanwhile, will sign on a season-long loan - with Everton paying a loan fee of £2m for the Portuguese worldwide midfielder. Everton always was a big option for me, especially after speaking with the coach, Marco Silva. Manchester United academy graduate Michael Keane had failed to be a solution for Everton upon joining from Burnley, while Ashley Williams and Phil Jagielka were clearly past their best.