Trautmann passed away on Friday morning in his adopted home of La Llosa, Spain, near Valencia.
The German football federation (DFB) said Trautmann had suffered two heart attacks this year and that it had been informed of his death by his wife, Marlies.
The City hero, who served with the Luftwaffe as a young man, arrived in England as a prisoner of war during World War Two but decided against returning to Germany following the end of hostilities.
Though his links with the German military initially led to some discontent amongst supporters, Trautmann won over City fans with his committed performances – no more so than that famous day at Wembley in 1956.
In the FA Cup final, Trautmann dived at the feet of Birmingham’s Peter Murphy and suffered a blow to the neck which knocked him unconscious.
In an era before substitutes, Trautmann bravely carried on and helped City record a famous 3-1 win before discovering he had broken his neck in the incident.
"Bert Trautmann was a great athlete and a true gentleman," said DFB president Wolfgang Niersbach. "He came as a soldier and thus an enemy to England but became a celebrated hero on the island.
"He was already a living legend. His extraordinary career will forever remain in the history books."
Trautmann was named Footballer of the Year in 1956 – the first player from outside Britain or Ireland to win the award – and finished his career with City in 1964.
He briefly managed Stockport in England as well as a number of teams abroad, and in 2004 was awarded with an OBE for his efforts in improving Anglo-German relations.
A City club statement read: "A true legend in the true sense of the word and a wonderful ambassador for not only his country, but Manchester City Football Club.
"Bert will be greatly missed by everyone who knew him and the football world in general."
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