Trautmann was born and raised in Germany, captured by the British during World War Two and turned down an offer of repatriation in 1948.
He went on to play for City from 1949 to 1964, winning the FA Cup when he broke his neck in the final against Birmingham City and managed to play on.
He was named England's Footballer of the Year at the end of that season.
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"Bert Trautmann was a great sportsman and a real gentleman," said DFB president Wolfsgang Niersbach.
"His extraordinary career will remain in the history books for ever."
The DFB said that Trautmann died at his home in Spain.
(Reporting by Brian Homewood in Berne, editing by Justin Palmer)
