The 23-year-old World Cup winner will sign a five-year contract starting on July 1, Bayern said in a statement. 

The 80 million euro fee makes him the most expensive signing in Bayern's history, almost doubling the sum paid for Corentin Tolisso. 

It also makes Hernandez one of the most expensive defenders in history, and one of the most expensive players ever signed by a German club.

"I am very happy that we have managed to sign Lucas Hernandez, who is a World Cup winner and one of the best defensive players in the world," said Bayern sporting director Hasan Salihamidzic. 
"Lucas can play in central defence or at left-back. He will strengthen our team and continue the tradition of fantastic French players at our club."

Bayern were knocked out of the Champions League in the round of 16 and Hernandez could be the first signing in an expected overhaul of the squad.

Hernandez has had a knee problem for a while. He has not played for Atletico since Feb 9 and missed France's recent internationals. 

Bayern said that he would undergo an operation on Wednesday after a medical exam revealed a problem with his knee. 

"Our medical examination revealed damage to Lucas Hernandez' right knee, which will have to be operated on," said Bayern team doctor Hans-Wilhelm Mueller-Wohlfahrt, confirming that Hernandez would, nonetheless, be fit to play by the start of next season. 

Hernandez signed for Atletico Madrid as a youth player in 2007, and has made 110 senior appearances for the club since his first team debut in April 2014. Last summer, he was a key player in France's World Cup winning campaign. 

"This is a very important day in my footballing career," said Hernandez.
"Bayern are one of the best clubs in the world. I will be proud to compete 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 12 wonderful years in Madrid," he said. 
"Atletico will always be a part of me, but I am now happy to be making the next step at Bayern."