The Bayern hierarchy are expecting the 57-year-old Ancelotti to keep the Bavarian giants, who kick off the new season at home to Werder Bremen on Friday, at the pinnacle of German football.
Guardiola quit for Manchester City at the end of last season, after sealing a third consecutive league title and the German Cup.
Heynckes had signed off by delivering Bayern's first major treble in 2013 when they lifted the Champions League, Bundesliga and German Cup titles.
Bayern's 2-0 victory at Borussia Dortmund ten days ago gave them the German Super Cup title, ending a run of three successive defeats in the season-opener under Guardiola.
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Like Heynckes before him, Italian Ancelotti has a reputation of being a father-figure, who instills confidence in his players, in contrast to Guardiola, who dishes out specific instructions.
Bayern regard themselves as a family club and Ancelotti has already followed that tradition by appointing his son Davide, a former AC Milan youth-team player, to his back-room staff, as he did during his spell at Real Madrid.
"Under Ancelotti, I finally feel like I'm trusted again," winger Franck Ribery told German magazine Kicker, before taking a swipe at Guardiola.
"I don't need a coach to tell me what I have to do right on the pitch when I have the ball," said Ribery in reference to Guardiola, which earned him a ticking off from Bayern chairman Karl-Heinz Rummenigge.
- 'A friend and a coach' -
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But Ribery is not the only player to criticise Guardiola during his time with Bayern - Stoke City winger Xherdan Shaqiri left Munich in 2015, suffering from a lack of belief from his coach.
In contrast, Ancelotti will start with Bayern having been given the seal of approval by some of football's big names.
"He just knows how to treat a man," said Zlatan Ibrahimovic, who worked with Ancelotti at Paris-Saint Germain.
"He is not just your trainer, he is your friend. It's incredible."
And Cristiano Ronaldo was full of praise for Ancelotti's style after the Italian won the Champions League title in the first of his two seasons with Real Madrid in 2014.
While Guardiola has won six league titles, three each with Barcelona and Bayern, Ancelotti has just three -- in Serie A with AC Milan in 2004, the Premier League with Chelsea in 2010 and Ligue 1 with PSG in 2013.
But Ancelotti has won the Champions League three times, including twice with AC Milan, while Bayern slipped to three successive semi-final defeats under Guardiola's tutelage.
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