The 26-year-old was in outstanding form for Napoli during the 2022-23 campaign, making 45 appearances in all competitions, including 35 outings in the team's Serie A title-winning season.
Manchester United were thought to be at the head of the queue for Kim, but it has now been confirmed that Bayern have won the race for his signature, securing his services on a deal until June 2028.
"Minjae Kim has developed extremely well, winning the Serie A title with Napoli last season and being voted the best defender in the league," Bayern CEO Jan-Christian Dreesen said in a statement.
"He impresses with his physical presence, as well as his mentality and speed. We're pleased he can immediately take part fully in pre-season and firmly believe that he will also excite our fans with his style of play."
Meanwhile, Kim added: "FC Bayern is a dream for every footballer. I'm really looking forward to what's to come in Munich. It's a new beginning for me.
"I'll continue to develop here. In discussions with the club, it was made clear to me from the start how interested they are in me. My first goal is to play a lot of games. In addition, I want to win as many trophies as possible."
The South Korean only made the move to Napoli from Fenerbahce last July, and he took to social media to say goodbye to the Italian club's fans.
"I sent this message to all the Napoli fans who have shown love and support," Kim wrote on his official Instagram account. "Thanks to you that Scudetto was possible after [Diego] Maradona, 33 years ago.
"To my passionate club Napoli, Mr [Luciano] Spalletti, my team mates and above all to Napoli fans, I would like to express my gratitude.
"No matter where I will be or no matter where I go, I will remember Napoli and cheer for you. Grazie. Forza Napoli sempre."
Bayern are believed to have activated a €50m (£43.4m) release clause which existed in his Napoli contract in order to bring him to Allianz Arena this summer.
Thomas Tuchel's side also remain hopeful of signing Harry Kane this summer, although Tottenham Hotspur chairman Daniel Levy is allegedly still insisting that the England captain is not for sale.