They beat Paris St-Germain to reach the Champions League quarter-finals, where they will face Manchester City.

Tuchel, 49, was sacked by Premier League club Chelsea in September.

He replaces Nagelsmann on a contract until 30 June 2025 and will take training for the first time on Monday.

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."

Nagelsmann, 35, joined Bayern after a spell at RB Leipzig and won the league by eight points in his first season in charge. He also led the team to back-to-back German Supercup wins.

But a 2-1 defeat by Bayer Leverkusen on Sunday left them with just five wins from their past 10 league games.

Assistant coaches Dino Toppmoller, Benjamin Gluck and Xaver Zembrod have also left the club.

Tuchel won the Champions League with Chelsea in May 2021 - one of three trophies won in 20 months at Stamford Bridge - and was voted World Coach of the Year following that campaign.

But the German, also formerly of Borussia Dortmund and Paris St-Germain, was sacked on new Chelsea owner Todd Boehly's 100th day in charge, following a 1-0 defeat by Dinamo Zagreb in the Champions League.

Bayern's next game is against league leaders Dortmund on Saturday, 1 April.

'Bayern's clear plan popped like a bubble' - analysis

Lutz Pfannenstiel, who worked with Nagelsmann at Hoffenheim, told BBC Sport his former colleague would not be short of offers.

"Julian is a strong personality and he is a top-level, world-class coach," said Pfannenstiel - now the sporting director of St Louis City SC. "After a little break, the offers will fly in left, right and centre.

"I think his next destination will be a foreign club, after all where can he go in the Bundesliga from Bayern Munich? With Julian following the English Premier League a lot that's definitely one of the potential markets.

"Bayern were worried about ending up without the title this season and if you really want to change a coach it's the right moment because it's the international break.

"But on the other hand you could say it's a crazy moment because you've just eliminated PSG, and especially considering he signed a five-year contract. That was a massive commitment by the club to change the playing style to the Nagelsmann style.

"There was a certain clear plan there and very suddenly it's popped like a bubble."