No details on on Vidal's contract length have been made official as yet, buts sources have told ESPN Barcelona could could get up to €1 million in variables from the deal.
The 33-year-old arrived in Milan ahead of his move on Sunday, with Inter's Twitter account posting photos of him at the airport.
Prior to Vidal's departure being made official, Barca captain Lionel Messi paid tribute to his former teammate in a post on Instagram.
"I only knew you from playing against you and I always thought you were a phenomenon but after being lucky enough to get to know you personally you surprised me even more," Messi wrote.
"We shared many things in the last two years and you made a huge impact on the dressing room and will be dearly missed. I wish you all the best luck in your new club and I'm sure our paths will cross again."
Vidal has since won a further five league titles -- two more with Juve, three with Bayern Munich followed one in Spain with Barca.