The 25-year-old has failed to establish himself in Barça's midfield since joining from rivals Valencia two years ago, making just 46 appearances in the league during that time.
His lack of game time resulted in his exclusion from Portugal's World Cup squad this summer, just two years after he helped his country win the 2016 European Championships.
The announcement of his signing comea amidst a flurry of late activity on Merseyside, as the club also confirmed the acquisitions of former Shakhtar Donetsk winger Bernard on a free transfer, alongside fellow Barcelona player Yerry Mina for £28.5m.
The Blaugrana pair were reported to have conducted their medicals simultaneously in the Spanish city, after Evertonian emissaries had flown over to finalise the deals.
That takes the Merseyside club's cumulative summer transfer window business up to five, following the previous acquisitions of Watford's Richarlison and Barcelona's Lucas Digne for a combined £58m.