Bayern have not revealed any details of the deal that sees Vidal arrive from last season???s Champions League finalist Juventus.
Vidal has experience of playing in the Bundesliga for Bayer Leverkusen, where he scored 15 goals during four seasons for before leaving for Juventus in 2011.
The 28-year-old is expected to fill the gap left by the departure of Bastian Schweinsteiger for Manchester United, and to give Pep Guardiola’s team more toughness.
Vidal was brought to Germany at age 20 from Chilean club Colo-Colo by Michael Reschke, who was squad director at Leverkusen.
Reschke ended his 35-year association with Leverkusen when Bayern appointed him as a director in June.
Vidal helped Juventus to four consecutive Serie A titles during his time in Italy, and the Coppa Italia last season.
He has been capped 69 times by Chile, and helped the team to a first Copa America success in July by scoring in the penalty shootout win over Argentina in the final.