Vidal has joined the San Siro outfit on a two-year contract with the option to extend for another year.
The 33-year-old Chilean international spent two years with Barcelona after joining from Bayern Munich in the summer of 2018 and won the Spanish La Liga title in his debut season.
A statement on Barcelona's website read: "FC Barcelona would like to publicly express their gratitude to Arturo Vidal for his commitment and dedication and wishes him all the best for the future."
The former Bayer Leverkusen midfielder’s move to Inter sees him reunite with manager Antonio Conte. The pair won three Scudetto titles together at Juventus during Vidal’s previous stint in Italy between 2011 and 2015.
A statement on the Inter Milan website announcing the Mohawk-wearing enforcer’s arrival read: "Arturo Vidal is officially an Inter player.
"The Chilean midfielder has joined Inter on a permanent deal from FC Barcelona. From today, Vidal will be on the front line for the Nerazzurri, with the same objectives as ever: fighting, giving it his all, and winning.
"He will become the sixth Chilean to play for Inter. The first was Ivan Zamorano, another born fighter. He was followed by David Pizarro, Luis Jimenez, Gary Medel and Alexis Sanchez.
"It’s confirmed. He’s arrived in Milan, and he’s a Nerazzurri player. Welcome to Inter, Arturo!"
Inter, who finished runners up in both the Serie A and Europa League last season, begin their league campaign with a home game against Fiorentina this weekend.