The 28-year-old posted a picture of himself and agent Fernando Felicevich on Twitter on Monday sat on a plane with the caption: “A new stage… a new dream… Munich here we come.”
Vidal is now expected to pass a medical to complete the deal, which Bayern chairman Karl-Heinz Rummenigge confirmed was imminent last Thursday.
A key component in the Juventus team that reached last month’s Champions League final, Vidal is expected to slot into Bayern’s midfield as a replacement for Germany captain Bastian Schweinsteiger, who has joined Manchester United.
Vidal is set for his second stint in the Bundesliga, having spent four seasons at Bayer Leverkusen from 2007-2011.
He converted a spot-kick in Chile’s 4-1 penalty shoot-out win over Argentina in the Copa America final earlier this month and was named in the team of the tournament.
However, his tournament was also overshadowed by an arrest for drink driving after he crashed his Ferrari as he was returning to the capital Santiago after an evening at a casino.
German champions Bayern have just completed a tour of China and will start the new Bundesliga season at home to Hamburg on Friday, August 14.
They will be bidding to make history by becoming the first team to win four consecutive Bundesliga titles.