During a glittering career, Mueller scored a record 365 goals for Bayern in the Bundesliga during the 1960s and 70s, as well as scoring 68 times for West Germany in 62 internationals.
"Today is a sad, black day for FC Bayern and its fans," said Bayern president Herbert Hainer.
"Gerd Mueller was the greatest striker there has ever been - and a fine person, a personality in world football.
"Without Gerd Mueller, FC Bayern would not be the club we all love today.
"His name and the memory of him will live on forever."
For the last few years, Mueller had been suffering from dementia.
He leaves behind his wife Uschi and a daughter.
Largely thanks to his goals, Mueller made history for both Bayern Munich and West Germany.
He scored an unbelievable 566 goals in 607 competitive games for FC Bayern.
He was part of Bayern teams which won four Bundesliga titles and dominated the former European Cup -- now the Champions League -- lifting the trophy three consecutive seasons from 1974-76.
Mueller's Bundesliga record of 40 goals scored in a single season stood from 1971/72 until current Bayern striker Robert Lewandowski scored for the 41st time in 2020/21 last May.
With the West German national team, Mueller won the 1972 European championships and the World Cup on home soil in 1974, scoring the winning goal in the final in Munich against the Netherlands.
After his career, he stayed with the club for a long time as a coach for the youth teams.
