The Blues look to have won the race to sign the former Shakhtar Donetsk man, who is expected on Merseyside to complete a medical and finalise personal terms on Tuesday.
Bernard, 25, rejected Shakhtar's offer of a lucrative new contract, and had been attracting serious interest from a number of clubs across Europe, including West Ham and Inter Milan.
Everton, though, are his preferred choice, and he is now set to become the third major signing of the Marco Silva era at Goodison Park.
He has already brought in another Brazilian, Richarlison, in a £40million ($52m) deal and last week spent around £18m ($23m) to bring Lucas Digne to the club. More are expected to follow this week.
Bernard, who can play as a wide player or centrally as an attacking midfielder, has built a stellar reputation during five seasons at Shakhtar, where he made more than 150 appearances, including 43 in European competition. He has 14 caps for Brazil, though the last of those came in 2014.
Silva remains keen to sign a centre back, with Manchester United's Marcos Rojo and Barcelona's Yerry Mina still on his radar. A central midfield player, too, would be a welcome addition, though the manager appears to have missed out on one target, Abdoulaye Doucoure, who has penned a new contract with Watford.