Nagelsmann, 35, led Bayern to the quarter-finals of the Champions League and will face Premier League champions Manchester City next month.
But Bayern have not enjoyed their normal dominance of the Bundesliga so far this season and so have replaced Nagelsmann with 49-year-old Tuchel, who won the Champions League with Chelsea in 2021.
The reigning German champions said in a statement: “FC Bayern and head coach Julian Nagelsmann have parted company… Nagelsmann will be succeeded by Thomas Tuchel.”
Bayern said Tuchel would receive a contract until June 2025 and he will supervise training for the first time on Monday.
Bayern chairman Oliver Kahn said: “Personally and on behalf of FC Bayern, I would like to thank Julian and his coaching team, and wish everyone the best of luck for the future.”
Bayern signed Nagelsmann to a five-year deal just two years ago but nerves have been fraying as the perennial Bundesliga champions struggle to hold onto their title.
They sit second to Tuchel’s former club Borussia Dortmund in the league table.
Tuchel — who Bayern had eyed previously but lost out to other top-flight European clubs — has been in between jobs after he was fired by Chelsea in September.
His first match will come as soon as April 1, when Bayern meet Dortmund, the club that Tuchel led from 2015-2017 before he left for PSG.
Although Bayern beat PSG in the last 16 of the Champions League, dumping out a team including Kylian Mbappe, Neymar and Lionel Messi, the Germans then suffered a blow when they lost 2-1 against Bayer Leverkusen last Sunday.
Bayern’s sporting director Hasan Salihamidzic gave a withering assessment of the team after that, saying the players had “so little drive, mentality, tackling, assertiveness”.
With just nine games left in the season, Nagelsmann himself had said that the Dortmund match would be a “must-win game”, but he has been relieved of his duties.
A coach considered one of the best young talents in Europe will probably not lack for offers from other clubs, and his departure will not go unnoticed by cash-rich clubs in England.
Tuchel has a reputation for occasional abrasiveness and demands total backing from his employers — a requirement which strained relations at both Chelsea and PSG.
He guided Chelsea to the Champions League title when they beat Manchester City 1-0 in the final in Porto in 2021, but was released by the London club soon after the start of this season and replaced by English manager Graham Potter.
Tuchel had been spotted in Munich in the last few weeks, fuelling widespread speculation that he was in talks with Bayern.