The 23-year-old, who has agreed a five-year contract with Bayern, had been on the wish list of several major European teams after he was part of France's 2018 World Cup-winning side.
"I am very happy that we managed to get one of the best defenders in the world and a world champion," said Bayern sports director Hasan Salihamidzic. "Lucas can play both as a central defender as well as a left back."
Hernandez will undergo surgery later on Wednesday, Bayern said, after his medical revealed some ligament damage in his right knee.
The club doctor, Hans-Wilhelm Mueller-Wohlfahrt, said he would be ready for start of next season. The player will refresh Bayern's backline, which has faced some criticism this campaign.
Current central defenders Jerome Boateng and Mats Hummels have been far from their 2014 World Cup-winning best and have recently been dropped from the Germany national team.
Bayern have endured an inconsistent season having spent little during the last two transfer periods and lost to Liverpool in the Champions League Round of 16 in their earliest exit from the competition in years.
They are level on 60 points with Borussia Dortmund at the top of the Bundesliga.
"Today is a very important day in my career," said Hernandez. "I am proud to be fighting for titles for Bayern in the future. I want to thank Atletico, the management, team mates and the fans for 12 wonderful years."
(Reporting by Karolos Grohmann; Editing by Christian Radnedge and Toby Davis)
