The 72-year-old returns to Bayern for a fourth spell in charge after the dismissal of Carlo Ancelotti at the end of September, with the Italian's last game a 3-0 UEFA Champions League defeat to Paris Saint-Germain.
Reports quickly began to point to Heynckes as Bayern's first-choice replacement and, after confirming he had received an offer on Thursday, the experienced coach is now in place to take charge for the remainder of the season.
Heynckes has not had a job in football since guiding Bayern to a historic treble in 2013, but confessed he simply could not turn the club down.
"I would not have returned to any other club in the world," he told Bayern's official website.
"But Bayern Munich is like a love affair for me. My coaching team and I will now do everything to present successful football to the fans again. I am very much looking forward to this task."
Hoffenheim coach Julian Nagelsmann is already being touted as a potential long-term successor, but Bayern chairman Karl-Heinz Rummenigge has no doubt Heynckes is the right man for the time being.
"Between Jupp Heynckes and Bayern there is a great deal of trust," said Rummenigge.
"The conversations that [club president] Uli Hoeness, [sporting director] Hasan Salihamidzic and I have now had have also shown this again.
"We are very grateful to Jupp for being the coach. He is the ideal coach for Bayern at the moment."