Tuchel is said to have been in talks with Tottenham Hotspur.
However, Bayern beat Spurs to the German tactician and he has now been unveiled as Julian Nagelsmann's replacement.
Bayern are one point off the top of the Bundesliga.
The Bavarians will also play Manchester City in the Champions League quarter-finals.
Current Spurs boss Antonio Conte is facing the sack following his recent outburst, with the Italian being unpopular with many of their senior players.