Nagelsmann has been in charge of the Bavarians for less than two years after joining from RB Leipzig in the summer of 2021.
Nagelsmann, one of the brightest young coaches in European football, won the Bundesliga title in his first season as well as two German Super Cups.
Bayern Munich have won the last ten Bundesliga titles but trail Borussia Dortmund by a point going into the international break.
They are into the quarterfinals of the UEFA Champions League, where they will face Manchester City.
Bayern chief executive Oliver Kahn said: "When we signed Julian Nagelsmann in the summer of 2021, we were convinced we would work with him on a long-term basis - and that was the goal of all of us right up to the end.
"But now we have come to the conclusion that the quality in our squad - despite the Bundesliga title last year - has come to the fore less and less often.
"After the World Cup we have played less successfully and less attractively. The big fluctuations in performance have cast doubt on our goals for this season, but also our goals for the future.
"That is why we have acted now. Personally and on behalf of Bayern, I would like to thank Julian and his coaching team, and wish everyone the best of luck for the future."
Tuchel has signed a contract until the summer of 2025.
He was without a club after Chelsea sacked him in September.
Tuchel's first game in charge of Bayern will be against his former club Borussia Dortmund on April 1.
