The Chilean midfielder will sign a three-year contract with the Blaugrana and have a medical to complete his move after the clubs agreed a fee.
Barcelona have reached an agreement to sign Arturo Vidal from Bayern Munich on a three-year contract.
While Inter and Milan were also offered his services, Barcelona have now closed the deal for Chilean star.
"FC Barcelona and FC Bayern Munich have reached an agreement for the transfer of player Arturo Vidal," read a statement on Barca's official website.
"The agreement with Arturo Vidal is for the next three seasons and is pending medical review that the player will pass in the coming days.
Ernesto Valverde signalled his intention to add to his midfield options after the Brazilian's departure, with club great Andres Iniesta having also departed for Asia by signing for Japanese side Vissel Kobe.
Arthur's move from Gremio was fast-tracked and Barca were reportedly interested in signing Adrien Rabiot from Paris Saint-Germain.
Injuries restricted Vidal to 17 Bundesliga starts in the 2017-18 season and he was linked with a January move to Chelsea, despite indicating he was willing to extend a Bayern contract that was set to expire at the end of this season.
He becomes Barca's fourth major signing of the transfer window, following Arthur, Bordeaux winger Malcom and Sevilla defender Clement Lenglet to Catalonia.
But they turned to Vidal after being unable to prise the France international away from the Ligue 1 champions.