The full-back, who played all but 40 minutes of Les Bleus’ World Cup winning campaign, has agreed a five-year deal with the Bundesliga champions which will be completed in the summer.
Hernandez, 23, becomes the second defensive recruitment Bayern have made for next season, with his French team-mate Benjamin Pavard also agreeing a £31million deal to join the Bavarian club from Stuttgart in January.
“Today is a very important day in my football career,” Hernandez said in a statement released by his new club
“Bayern Munich is one of the best clubs in Europe and the world. I am proud to be able to fight for all titles for Bayern in the future.
“I would like to thank Atletico, the management, the coaches, my team-mates and the fans for a wonderful 12 years. Atletico will always be part of me. Now I’m happy that I’m taking the next step at Bayern.”
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Hernandez leaves Atletico having emerged as a key member of Diego Simeone’s defence in the Spanish capital.
The full-back has made 67 LaLiga appearances for the Colchoneros, scoring one goal, but will play no further part this season after sustaining a knee ligament injury.
Hernandez started his career at Rayo Majadahonda before moving to Atletico’s youth system in 2007 and breaking through the ranks to cement a spot on the left-side of defence.
The deal sees Hernandez become the second most expensive defender in history, behind only Virgil van Dijk, who joined Liverpool from Southampton for £75million last year.