Lucas Hernandez will join Bayern Munich on July 1 on a five-year deal running through to June 2022.
Hernandez broke through the youth ranks at Atletico in 2014 and went on to collect 67 appearances for the La Liga club, as well as 15 caps for his country.
“I am very happy that we have been able to sign one of the best defensive players in the world and world champion in Lucas Hernandez,” said Bayern sporting director Hasan Salihamidzic.
“Lucas will continue our tradition of outstanding French players and strengthen our team.”
Hernandez will undergo surgery on his right knee after revealing ligament damage during his medical with Bayern.
His £68m price tag overtook the £37m that Bayern spent for Corentin Tolisso from Lyon in 2017 and the potential £47m overall that they would pay if they exercise the option to buy James Rodriguez from Real Madrid.
“Today is a very important day in my football career,” said Hernandez.
“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 twelve years. Atletico will always be a part of me. Now I’m happy that I’m taking the next step at Bayern.”