"I am very proud to be joining Paris Saint-Germain," the 25-year-old told his new club's official website.
"Paris Saint-Germain are known throughout Europe, with world-class players."
Additionally, Bernat cited the importance of PSG head coach Thomas Tuchel in his decision, having gone up against his Borussia Dortmund sides with Bayern.
"I am also looking forward to working under Thomas Tuchel, whose work in Germany was remarkable. I am truly excited to be taking the next step of my career with Paris."
Bayern sporting director Hasan Salihamidzic said: "Juan Bernat has asked us to accept the offer from Paris and to release him from his contract. We have complied with this request and have reached an agreement with PSG in very good talks.
"Juan has always been a model pro and played a big part in the eight titles we've won with him. We wish him and his family all the best in Paris."
Tuchel is expected to further bolster his squad with the surprise acquisition of Eric Maxim Choupo-Moting from Stoke City before the transfer window closes.