Capable of playing in midfield or at full-back, Kimmich joined from RB Leipzig in 2015 and has gone on to win 17 trophies with Bayern, who are chasing a 10th successive Bundesliga title this season.
He had two years left to run on his previous deal, though talks had been ongoing over a long-term extension.
Last week, club president Herbert Hainer insisted Bayern would not bow to excessive demands, even to keep such talents as Kimmich and his midfield partner Leon Goretzka, whose deal runs out at the end of 2021-2022.
"They will certainly not be kept at any cost," Hainer told Kicker. "The players know what they have at Bayern, they are paid very well here too, everyone gets their salary.
"And they can win titles with us now, and also in the future."
It appears any impasse in negotiations with Kimmich was swiftly resolved, however, with the 26-year-old agreeing terms on a two-year extension.
"The most important reason for my contract extension is that I can pursue my passion with joy every day here at FC Bayern," Kimmich said.
"I have a team where I can achieve everything, and a lot of team-mates have become real friends. That’s why I started playing football in the first place, because it should be fun.
"I still don't think I'm at the end of my development and I'm convinced there's a lot possible at FC Bayern in the next years.
"On top of that, my family feels at home here. Munich has become a second home. The combination we have here isn’t found all over the world."
Bayern sporting director and board member Hasan Salihamidzic, meanwhile, believes securing Kimmich on fresh terms is a clear message of intent.
"With this contract extension, Bayern is sending a clear signal, both internally and externally," he said.
"We want to sign our best players over the long term. Joshua will develop his great quality as a leading player at Bayern in the next few years and make history."