Mueller netted 68 goals in 62 internationals, including the winner in the 1974 World Cup final, and is third in the all-time list of most goals in the global showpiece tournament with 14, behind Brazilian Ronaldo (15) and German Miroslav Klose (16).
"He was the "Bomber der Nation", Germany's biggest goal scorer ever," the German FA said.
Having joined Bayern Munich in 1964, Mueller - an instinctive striker who was good in the air and quick on his feet - scored 566 goals in 607 matches spread over 15 years with the club.
Mueller netted a record 365 goals in the Bundesliga in a trophy-laden career that included four league titles, four German Cups and three European Cups with Bayern.
He won the Golden Boot after scoring 10 goals at the 1970 World Cup before collecting the Ballon d'Or that year and an uncanny ability to turn and score from seemingly impossible angles became Mueller's trademark.
He also helped West Germany win the 1972 European Championship.