The German giants did not disclose the transfer fee but according to German and Italian media Bayern had paid a release clause worth 50 million euros ($56.11 million) for the player.
"FC Bayern is a dream for every footballer," Kim told the club website.
"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."
Kim, who joined Napoli from Turkish side Fenerbahce in July last year, was a vital part of the team that won the Scudetto for the first time in more than three decades last season.
"Kim Min-jae 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.
"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."
In Napoli, Kim played 45 matches in all competitions, scoring two goals.
He announced he had left the Italian side earlier on Tuesday.
"I send this message to all the Napoli fans who have shown love and support. Thanks to you the Scudetto was possible after (Diego) Maradona, 33 years ago," Kim said in a statement on Instagram.
"To my passionate club Napoli, Mister (manager Luciano) Spalletti, my teammates, 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."
Kim has earned 49 caps for South Korea since making his debut back in 2017. However, he was unable to participate in the last two friendlies due to military service.
