Muller won the 1972 European Championship, the 1974 World Cup, a Club World Cup, three European Cups, a European Cup-Winners' Cup, four Bundesliga titles and four German Cups. He also won the Ballon d'Or in 1970.
His total of 365 Bundesliga goals remains a German record, while his single-season high of 40 was beaten only by Robert Lewandowski last term.
"Today is a sad, black day for FC Bayern and all of its fans. Gerd Muller was the greatest striker there has ever been -- and a fine person, a personality in world football," Bayern president Herbert Hainer said in a statement.
"We are united in deep sorrow with his wife Uschi and his family. Without Gerd Muller, FC Bayern would not be the club we all love today. His name and the memory of him will live on forever."
Muller scored 14 goals at two World Cups and, in 1972, hit 85 goals in only 60 matches for club and country. That remained a world record until Lionel Messi struck 91 times in 69 matches in 2012.
"Records don't mean much to me, but if someone deserves to surpass me, then it's Messi," Muller said at the time.
The forward, nicknamed Der Bomber der Nation -- the Bomber of the Nation -- scored 68 goals in 62 games for Germany, making him their top scorer until Miroslav Klose surpassed his total in 2014.
His most important goal came in the 1974 World Cup final, when he scored the winner in typical style with a quick turn and finish in a 2-1 win over Netherlands, his last game as a West Germany international.
Born in Nordlingen, Bavaria, on Nov. 3, 1945, Muller did not play football at the club level until he was 12, when he joined his hometown side.
FC Bayern are mourning the passing of Gerd Müller.— FC Bayern English (@FCBayernEN) August 15, 2021
The FC Bayern world is standing still today. The club and all its fans are mourning the death of Gerd Müller, who passed away on Sunday morning at the age of 75.
He moved to Bayern in July 1964 and played a key role as they were promoted to the Bundesliga the following year, scoring 39 goals in the 1964-65 season.
In his first year in the German top flight, he scored 15 goals in 33 games -- his worst career return. Muller went on to become the league's top scorer in seven of the next 14 seasons.
When he left Germany for American club Fort Lauderdale Strikers in early 1979, he had scored 365 goals in 427 games for Bayern.
No other Bundesliga player has come close to that tally, with Bayern's Lewandowski, the player with the best modern record, on 278 goals in 351 games.
"The news of Gerd Muller's death affects us all deeply. He is one of the greatest legends in the history of FC Bayern, his achievements are unmatched to this day and will forever be part of the great history of FC Bayern and all of German football," Bayern CEO Oliver Kahn said in a statement.
"As a player and as a person, Gerd Muller stands like no other for FC Bayern and its development into one of the largest clubs in the world. Gerd will be in our hearts forever. "
After three years at Fort Lauderdale, Muller retired in 1981. Returning to Germany a few years later, he struggled with post-playing life and slowly descended into alcoholism.
He overcame his addiction with the help of his old club Bayern, where he held several minor positions before being diagnosed with Alzheimer's disease in the early 2010s.
Muller made his last public appearance at an awards ceremony in 2013 and, two years later, Bayern confirmed reports that he had Alzheimer's.
In April 2019, Muller was inducted into the Hall of Fame of German football.
Former Bayern and Germany teammate Paul Breitner, who accepted the accolade on Muller's behalf, said: "The unbelievable success story of Bayern Munich and the German national team would be unthinkable without Gerd Muller."