The club's hierarchy held a meeting to discuss Ancelotti's future on Thursday afternoon and he has now left the Bavarians.
The former Chelsea chief guided Bayern to the Bundesliga title last season but crashed out of the Champions League to Real Madrid at the quarter-finals stage.
Carlo Ancelotti has been dismissed as manager of Bayern Munich after their 3-0 humiliation at the hands of PSG.
Bayern were swept aside by French giants PSG, who recorded a comprehensive 3-0 Group B victory thanks to expensively-assembled attacking trio Edinson Cavani, Neymar and Kylian Mbappe on Wednesday.
Bayern assistant coach Willy Sagnol will take over from Ancelotti as interim coach, while former Borussia Dortmund boss Thomas Tuchel has also been mentioned along with Hoffenheim coach Julian Nagelsmann also linked.
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"Since the start of the season, the performance of the team has not met our expectations, and the match in Paris has shown clearly that we had to make conclusions", Rummenigge stated.
"I think it's important to turn things around after this loss". I think it's important to turn things around after this loss, to present as Bayern Munich and to show we are a team, [the one] which performed well in Europe and in Germany past year.
It did not help Ancelotti's cause that he controversially benched senior players Mats Hummels, Arjen Robben and Franck Ribery. "I now expect the team to develop positively with absolute dedication so we can reach our goals for this season". In the first half, we had good control of the game, good possession, some chances.
Ancelotti led Real Madrid to its 10th Champions League title in 2014 after claiming two with Milan in 2003 and 2007, and he was appointed by the Bayern bosses primarily for success in Europe's premier competition. "I thought a lot about what the best team to play was".