Bayern surprisingly parted ways with Julian Nagelsmann (35) on Friday and wasted no time in bringing in former Chelsea coach Tuchel in a deal to 2025 as his replacement.
Bayern bosses blamed the team's performances in the past months for the sacking of Nagelsmann, with Bayern in second place in the Bundesliga.
They face Manchester City in the Champions League quarter-finals next month and are also through to the German Cup last eight.
"They are one of the best clubs in the world. Their DNA is about winning and also the way, but firstly about winning," Tuchel told a news conference.
"The responsibilities are clear and there is absolutely no misunderstanding. The squad assembled by Bayern is one of the most talented and best squads in Europe. You can challenge for every title with this squad."
"That puts me under pressure but at Bayern it's about winning all titles. We are here to win all the titles."
Tuchel's arrival comes just as Bayern prepare to face leaders Borussia Dortmund, one of Tuchel's former teams, next week in the Bundesliga and City in the Champions League quarter-finals on April 11.
"I would have liked to have a few more training sessions but I won't have too many looking at the schedule and the international break this week," Tuchel said.
"There is a chance to win all the titles. There is no need for big changes in the system or the processes."
Tuchel, a long-time Bayern target since their first attempt to sign him in 2018, won the Champions League for Chelsea in 2021 after replacing Frank Lampard, but has been without a job since being sacked by the English side last year.
He built a reputation as a forward-thinking tactician in the Bundesliga during his time at Mainz before taking over at Dortmund and leading them to German Cup success in 2017.
"He led Paris St Germain to the Champions League final, at Chelsea he was successful from the start, won the Champions League. That's an impressive CV," said Bayern CEO Oliver Kahn (53).
"That shows development so we are delighted that Thomas Tuchel is now our coach."
