Barcelona followed that news with confirmation that Portugal midfielder Andre Gomes would also be moving to the Goodison Park club on a season-long loan.
Playmaker Bernard arrived on a free transfer after his contract ended with the Ukrainian club while Barcelona said Everton had agreed to sign centre back Mina for an initial 30.3 million euros ($47m) and have taken midfielder Gomes on loan.
The report claims that Mina and Gomes have both completed medicals for the club and will be officially confirmed as Everton players shortly.
Barcelona have included a set buy-back option in their deal with Everton for Yerry Mina.
Bernard, also 25, has signed a four-year deal with the Merseyside club after his contract at Shakhtar ran out in June.
Southampton signed striker Danny Ings from Liverpool on a season-long loan before a permanent deal next year.
Moments later they also confirmed that Portugal worldwide Gomes would join the Premier League side on loan. This is a great opportunity for me and I am looking forward to competing here. But I was also convinced Everton could improve me and that I would be able to show my best as a player here'.
New Everton defender Yerry Mina says that he wants to win things with the Blues. Everton always was a big option for me, especially after speaking with the coach, Marco Silva.
Manchester United and Lyon had both tracked Colombia global Mina, who signed a five-year deal after Barca sanctioned his £27.2 million sale. 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.