Barca, who were initially reluctant to drop their £35 million ($47m) valuation of the Colombia international, have settled on a fee in the region of €32m (£29m/$37m) following a dramatic last 48 hours of developments in the player's future.
Marco Silva's side appeared to be on the verge of signing Mina, who starred for Colombia at the World Cup, on July 26, although turned their attentions to Marcos Rojo having been frustrated by Barca's initial refusal to lower their asking price.
Manchester United then emerged as possible suitors to sign the former Palmeiras defender, only for the Red Devils to pull the plug on their interest late on Saturday night, as they focused on other targets, namely Toby Alderweireld.
Silva's Everton had appeared not to be interested in returning to the negotiating table having been messed around by Barca in their attempts to sign Mina, with United's late interest having also muddied the waters.
But Goal understands that, with only a few days remaining of the transfer window in England, there has been a change of heart on Merseyside and the club quickly moved to agree a transfer in the region of €32m.
Mina, for his part, appeared to be out of options, with the 23-year-old behind the likes of Gerard Pique, Samuel Umtiti, Thomas Vermaelen and now new signing Clement Lenglet in the Camp Nou pecking order.
Reports in France have claimed that Lyon had joined the race for the towering centre-back, but he now seems all set to make the move to the Premier League, with the agreement of personal terms and a medical with the Toffees to follow.
The Merseysiders get their Premier League campaign underway on August 11 with a trip to newly-promoted Wolves.