The Chile midfielder has agreed a three-year contract at the Camp Nou and will undergo a medical in the coming days, the Spanish champions announced on their website.
Vidal joined Bayern from Juventus in 2015 and won the Bundesliga title in each of his three seasons at the club.
Neither club have announced a transfer fee for the 31-year-old – who was under contract at Bayern until June 30, 2019 – but reports in Spain suggest Barca will pay in the region of €20 million.
A Barca statement read: “Barcelona and Bayern Munich have reached an agreement for the transfer of player Arturo Vidal. The agreement is for the next three seasons and is pending the medical examination that the player will undertake over the course of the next few days.”
Vidal played 124 competitive games for Bayern, scoring 22 goals and providing 17 assists. As well as his three Bundesliga titles he also helped the German giants win the DFB-Pokal in 2016 and the German Super Cup twice.
The former Bayer Leverkusen player said on Bayern’s official website: “Thanks to FC Bayern and all the fans. I really enjoyed my time in Munich. I would like to thank the club for giving me another chance to take on a new challenge in Barcelona.”
Bayern chief executive Karl-Heinz Rummenigge added: “We celebrated great success during this time, and Arturo had a significant share in that. He has always been at the forefront of important games, we have always been able to rely on him.”
Earlier on Friday Barca announced they had agreed a deal to sign teenage Senegal defender Moussa Wague from Belgian side KAS Eupen.
The 19-year-old right-back, who has already passed his medical with Barca, played all three of Senegal’s games at this summer’s World Cup and his goal in the 2-2 draw with Japan saw him become the youngest African goalscorer in finals history.
Barca have already signed Arthur, Malcom and Clement Lenglet this summer, while Andres Iniesta, Paulinho, Lucas Digne and Gerard Deulofeu are among those who have left the Nou Camp.
In a statement on their website, the club said they have agreed a three-year deal with Vidal, who will be presented to the fans shortly.
For La Blaugrana, Vidal adds depth to a midfield that was stretched thin at times last season. He’s the second player in the position to join this summer, after Brazilian starlet Arthur, and reinforces a midfield corps that includes Sergio Busquets, Ivan Rakitic, and Philippe Coutinho – who could be pushed further forward thanks to the new arrival.
Burnley are interested in giving goalkeeper Joe Hart a Premier League lifeline, Press Association Sport understands.
The Clarets are keen to sign Hart, who will again not be part of Pep Guardiola’s plans at Manchester City.
Sean Dyche has yet to make any signings so far this summer, but has goalkeeping issues after his number one Nick Pope had shoulder surgery this week while Tom Heaton is coming back from a calf injury.
Hart, 31, has not played for City since August 2016 and has spent the last two seasons on loan at Torino and West Ham.
He struggled to reach the heights with the Hammers, though, and lost his place in the England squad for the World Cup, with Pope chosen in his place.
The deal, which is set to be a permanent one, could be completed over the weekend.