Tuchel, who became the first German coach to lead three different teams to the last four of the Champions League, will leave a year early after a disappointing domestic run.
Bayern will not win any domestic silverware this season after their 11-year reign as Bundesliga champions was ended by Bayer Leverkusen and their bad run led to club bosses to part ways with Tuchel at the end of the season.
"The semi-final is a huge step. The last four, that was fun. Great joy and great relief," Tuchel told a press conference.
"These are special moments. We beat one of the top Premier League clubs. We will have to see what this win does to the club. The season is not yet over. Especially not now."
The Bavarians won courtesy of Joshua Kimmich's 63rd-minute header that gave them a 3-2 aggregate win over the two legs, with Bayern president Herbert Hainer hailing Tuchel's coaching as 'a tactical masterpiece'.
They will next face Real Madrid in the last four after the Spaniards eliminated last year's champions Manchester City on penalties.
Wednesday's result means Tuchel has become the first German to lead clubs from three different countries to at least the semi-finals of the competition after he won the title with Chelsea in 2021 and led Paris St-Germain to the final in 2020.
Asked whether he felt any gratification given how his season had unfolded with Bayern, Tuchel said: "But where did the criticism come from? From you, the media, and now you ask me if I feel any gratification?"
"It is what it is. I have given it all from the first day and will give it all until the last day," he said.
Tuchel can now leave on a high with Bayern still in the running for the biggest continental club trophy which they have won six times before.
"We are very proud to have reached the semi-finals and we will now see in two weeks what will happen," he said.
