A stinging 3-0 defeat by Paris Saint-Germain in the Champions League led the club to sack Ancelotti.
Despite his age, Heynckes says he feels "fit" enough to coach Bayern, who he led to the Champions League, Bundesliga and German Cup treble in 2013.
The 72-year-old veteran manager had on Thursday confirmed to Rheinische Post, a local paper near his home that Bayern president Uli Hoeness and chief executive Karl-Heinz Rummenigge have asked him to return.
Jupp Heynckes poseing with four trophies after giving his farewell press conference in Munich, southern Germany, on June 4, 2013. His appointment had been delayed while Bayern waited for Hermann to be released by second-division club Fortuna Duesseldorf, where he was a coach. We are very grateful to Jupp for being taking a caretaker role.
Air France flight with engine damage makes emergency landing
The images appeared to show that the inlet, or front part, of the engine had torn off, but the main part of the engine was intact. The plane was about an hour off the coast of Canada when the incident occurred, Miguel Amador, a passenger on the flight, said.
Bayern split with Italian coach Carlo Ancelotti on September 28 due to the poor performance of the club, reports Efe.
Sports director Hasan Salihamidzic said: "Jupp Heynckes is a master of human rights and tactics".
Heynckes said: "I would not have returned to any other club in the world, but the FC Bayern München is a heart affair for me. I'm really looking forward to this task". Guardiola failed to win the Champions League in his three seasons, while Ancelotti's side was outclassed by eventual champion Madrid last season.
This will be Heynckes' fourth spell at the club, having previously been at the helm from 1987-1991, for a five-game spell in 2009, and again from 2011-2013.
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