The Toffees will pay Barca an initial €30.25m (£27m/$35m), plus potentially another €1.5m in variables for Colombian defender Mina. The Catalan side also have a buy-back option on the 23-year-old, who joined from Palmeiras in January.
Everton confirmed the pair of signings themselves later on Thursday.
Mina, a Colombia international who scored three goals at the World Cup, made only five league appearances as Barcelona won the title.
But he struggled to really establish himself in those outings and had been linked with a move away from Camp Nou since the end of last season. The centre-back fell even further down the pecking order when Barca brought in Clement Lenglet in July.
Manchester United had been strongly linked with Mina but pulled out to pursue other targets , while Lyon had held out hope of signing him until the end. Everton have finally got the deal over the line, however, with Barca announcing their agreement shortly before the Premier League's transfer deadline.
Meanwhile, Gomes will join Marco Silva's side after Everton agreed to pay €2.25m to land him on loan for the season, while they will also pay his wages.
The midfielder had also been unable to cement a spot in the first team since joining from Valencia in 2016 in a €35 million (£31m/$41m) deal.
The 25-year-old has opened up about his struggles at Barca, saying it felt like "hell" after the first six months.
Goal reported on Thursday that the Portugal international would have a medical in Spain before travelling to Merseyside before the close of the window.
Mina and Gomes are not the only players who have gone from Camp Nou to Goodison Park in the transfer window, as Lucas Digne made the switch earlier on.
It was a busy transfer deadline day for Everton, who also signed Bernard from Shakhtar Donetsk on Thursday, with the Brazilian winger signing a four-year contract.