The 58-year-old was shown the door after Paris Saint-Germain dispatched the German giants 3-0 in the Champions League, their second defeat in six competitive fixtures.
Ancelotti was already in the spotlight for a series of lacklustre performances and Bayern responded by severing ties with the decorated manager.
Having taken over from Pep Guardiola for the 2016-17 season, the Italian led Bayern to their fifth consecutive league title and also collected two DFL-Supercup trophies during his stay at the Allianz Arena.
"It has been a great honour to form part of Bayern's history. I would like to thank the club, the players and its amazing fans," Ancelotti wrote on Twitter.
Robert Lewandowski, Arturo Vidal and Thiago Alcantara are among the players to have paid tribute to their former boss on social media.
"It has been an honour to play for you. I wish you all the luck in the world for your next stage," midfielder Thiago posted.
French winger Franck Ribery, who earlier this month reacted angrily to being substituted against Anderlecht, simply wrote "Always Forward" on Instagram.